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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative Springer resolution; perverse sheaves on affine flag variety Bezrukavnikov, R.; Lin, Q., Highest weight modules at the critical level and noncommutative Springer resolution, Contemp. Math., 565, 15-27, (2012) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Geometric Langlands program: representation-theoretic aspects, Geometric Langlands program (algebro-geometric aspects), Quantum groups (quantized function algebras) and their representations Higher weight modules at the critical level and noncommutative Springer resolution
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Yagi J 2012 Chiral algebras of (0, 2) models \textit{Adv. Theor. Math. Phys.}16 1 Quantum field theory on curved space or space-time backgrounds, Supersymmetric field theories in quantum mechanics, Perturbative methods of renormalization applied to problems in quantum field theory, Nonperturbative methods of renormalization applied to problems in quantum field theory, Covariant wave equations in quantum theory, relativistic quantum mechanics, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Kähler manifolds, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.) Chiral algebras of (0, 2) models
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces factorization algebra; Chern-Simons theories; spacetime manifold; gauge group; deformation theory; differential graded algebra; moduli space Research exposition (monographs, survey articles) pertaining to quantum theory, Finite-dimensional groups and algebras motivated by physics and their representations, Homological algebra in category theory, derived categories and functors, Graded Lie (super)algebras, Topological quantum field theories (aspects of differential topology), Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Formal methods and deformations in algebraic geometry, Eta-invariants, Chern-Simons invariants Chern-Simons theory and equivariant factorization algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Pieri operators; Pieri formula; graded operation; Hopf algebra; quasi-symmetric functions; skew Schur functions; generating function; skew Schubert functions; Stanley symmetric functions; poset Bergeron, Mykytiuk, Sottile, and van Willigenburg, ''Non-commutative Pieri operators on posets,'' J. Combin. Th. Ser. A 91 (2000), 84--110. Symmetric functions and generalizations, Combinatorics of partially ordered sets, Classical problems, Schubert calculus Noncommutative Pieri operators on posets
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; noncommutative curve Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry An abstract characterization of noncommutative projective lines
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic group; homogeneous space; algebra of invariants Avdeev, R.S.: Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups. Izv. Math. \textbf{74}(6), 1103-1126 (2010), see also arXiv:1012.0132 [math.RT] Homogeneous spaces and generalizations Extended weight semigroups of affine spherical homogeneous spaces of non-simple semisimple algebraic groups
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces line scheme; point scheme; Lie algebra; superalgebra; regular algebra; Plücker coordinates Quantum groups (quantized enveloping algebras) and related deformations, Noncommutative algebraic geometry, Quadratic and Koszul algebras, Universal enveloping (super)algebras, Color Lie (super)algebras The quantum spaces of certain graded algebras related to \(\mathfrak{sl}(2, \Bbbk)\)
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces poset codes; poset metrics; Rosenbloom-Tsfasman metric; symmetries L. Panek, M. Firer, M. Muniz, Symmetry groups of Rosenbloom -- Tsfasman spaces, submitted for publication. Applications to coding theory and cryptography of arithmetic geometry, Finite automorphism groups of algebraic, geometric, or combinatorial structures, Geometric methods (including applications of algebraic geometry) applied to coding theory Symmetry groups of Rosenbloom-Tsfasman spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cyclic algebras; Arason invariant; biquaternion algebras; Albert form; corestriction of central simple algebras; quartic 2-extensions; Witt kernel; \(n\)-Pfister form; relative Brauer group; Galois cohomology Lam, T.Y.; Leep, D.B.; Tignol, J.-P., Biquaternion algebras and quartic extensions, Publ. math. IHéS, 77, 63-102, (1993) Quaternion and other division algebras: arithmetic, zeta functions, Finite-dimensional division rings, Brauer groups of schemes, Algebraic theory of quadratic forms; Witt groups and rings, Galois cohomology, Twisted and skew group rings, crossed products Biquaternion algebras and quartic extensions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces complex algebraic curves; \(C^\ast\)-algebras; Teichmüller space; foliations; continued fraction; stable isomorphism Nikolaev, Noncommutative geometry of algebraic curves Noncommutative geometry of algebraic curvesProc, Proc Amer Math Soc Amer Math Soc pp 137-- (2009) Families, moduli of curves (algebraic), Automorphisms of selfadjoint operator algebras, Noncommutative geometry (à la Connes) Noncommutative geometry of algebraic curves
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Rubenthaler, H., Algebras of invariant differential operators on a class of multiplicity-free spaces, C. R. acad. sci. Paris, ser. I, 347, 1343-1346, (2009) Harmonic analysis on homogeneous spaces, Rings of differential operators (associative algebraic aspects), Representation theory for linear algebraic groups, Geometric invariant theory Algebras of invariant differential operators on a class of multiplicity free spaces.
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cohomology theories; intersection cohomology; \(L^2\)-cohomology; weighted cohomology Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects), Analytic sheaves and cohomology groups, Cohomology of arithmetic groups, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Intersection homology and cohomology in algebraic topology On the cohomology of locally symmetric spaces and of their compactifications
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces locally symmetric spaces; sheaf; intersection cohomology; \({\mathcal L}^2\)-cohomology; Borel-Serre compactification; Satake compactification; stratified pseudomanifolds; \(\mathcal L\)-modules; Rapoport/Goresky-MacPherson conjecture; weighted cohomology Leslie Saper, On the cohomology of locally symmetric spaces and of their compactifications, Current developments in mathematics, 2002, Int. Press, Somerville, MA, 2003, pp. 219 -- 289. Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Modular and Shimura varieties, Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects), Cohomology of arithmetic groups, Intersection homology and cohomology in algebraic topology On the cohomology of locally symmetric spaces and of their compactifications
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative complex geometry; quantum projective space; quantum homogeneous coordinate ring; twisted cyclic cocycle; positive Hochschild cocycle; Serre duality Khalkhali M., Moatadelro A.: Noncommutative complex geometry of the quantum projective space. J. Geom. Phys. 61(12), 2436--2452 (2011) Noncommutative geometry in quantum theory, Noncommutative geometry methods in quantum field theory, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Projective analytic geometry Noncommutative complex geometry of the quantum projective space
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; noncommutative projective line; noncommutative curve; two-sided vector space; noncommutative symmetric algebras; arithmetic noncommutative projective line Nyman, A, The geometry of arithmetic noncommutative projective lines, J. Algebra, 414, 190-240, (2014) Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry The geometry of arithmetic noncommutative projective lines
| 1 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Krichever-Novikov algebras; meromorphic vector fields; theta functions; Weierstraß \(\sigma \) function M. Schlichenmaier, ''Krichever-Novikov Algebras for More Than Two Points: Explicit Generators,'' Lett. Math. Phys. 19, 327--336 (1990). Differentials on Riemann surfaces, Theta functions and curves; Schottky problem, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Krichever-Novikov algebras for more than two points: explicit generators
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces embeddings of blow-ups; Cohen-Macaulay property; graded Rees algebra; complete intersection ideal; diagonal subalgebra Aldo Conca, Jürgen Herzog, Ngô Viêt Trung, and Giuseppe Valla, Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces, Amer. J. Math. 119 (1997), no. 4, 859 -- 901. Cohen-Macaulay modules, Embeddings in algebraic geometry, Relevant commutative algebra, Polynomial rings and ideals; rings of integer-valued polynomials, Linkage, complete intersections and determinantal ideals Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative polynomials; noncommutative rational functions; linear matrix inequalities; determinantal representations J.\ W. Helton, S.\ A. McCullough and V. Vinnikov, Noncommutative convexity arises from linear matrix inequalities, J. Funct. Anal. 240 (2006), no. 1, 105-191. Several-variable operator theory (spectral, Fredholm, etc.), Semialgebraic sets and related spaces, Positive matrices and their generalizations; cones of matrices, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Linear inequalities of matrices, Algebraic methods Noncommutative convexity arises from linear matrix inequalities
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(C^*\)-algebra; general relativity; noncommutative geometry; singularities; Friedman model Heller, M., Sasin, W.: Noncommutative structure of singularities in general relativity. J. Math. Phys. 37, 5665--5671 (1996) Noncommutative topology, Noncommutative differential geometry, Space-time singularities, cosmic censorship, etc., Noncommutative algebraic geometry, General theory of \(C^*\)-algebras, Applications of global analysis to the sciences Noncommutative structure of singularities in general relativity
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Uhlenbeck spaces; Kac-Moody Lie algebras; \(G\)-bundles Braverman, A.; Finkelberg, M.; Gaitsgory, D., Uhlenbeck spaces via affine Lie algebras, (The Unity of Mathematics (Volume Dedicated to I.M. Gelfand's 90th Birthday), Progr. Math., vol. 244, (2006), Birkhäuser Boston), 17-135 Algebraic moduli problems, moduli of vector bundles, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras Uhlenbeck spaces via affine Lie algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Krichever-Novikov algebras; meromorphic vector fields; higher genus Riemann surfaces M. Schlichenmaier, ''Krichever-Novikov Algebras for More Than Two Points,'' Lett. Math. Phys. 19, 151--165 (1990). Differentials on Riemann surfaces, Curves in algebraic geometry, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Krichever-Novikov algebras for more than two points
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative projective scheme; cluster tilting module; AS-Gorenstein algebra; AS-regular algebra; ASF-regular algebra Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Cohen-Macaulay modules in associative algebras, Graded rings and modules (associative rings and algebras) Cluster tilting modules and noncommutative projective schemes
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces nilpotent cone; nilpotent varieties; symmetric spaces; twisted affine Schubert varieties Grassmannians, Schubert varieties, flag manifolds, Coadjoint orbits; nilpotent varieties Nilpotent varieties in symmetric spaces and twisted affine Schubert varieties
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Pieri rules; classical groups; tensor products of representations Howe, R., Kim, S., Lee, S.T.: Double Pieri algebras and iterated Pieri algebras for the classical groups (\textbf{preprint}) Representation theory for linear algebraic groups, Combinatorial aspects of representation theory, Semisimple Lie groups and their representations, Grassmannians, Schubert varieties, flag manifolds Double Pieri algebras and iterated Pieri algebras for the classical groups
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic cobordism; cohomological operations; Landweber-Novikov operations Vishik, A., \textit{symmetric operations in algebraic cobordism}, Adv. Math., 213, 489-552, (2007) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Algebraic cycles Symmetric operations in algebraic cobordism
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hodge modules; symmetric products Maxim, L.; Saito, M.; Schürmann, J., Symmetric products of mixed Hodge modules, J. Math. Pures Appl. (9), 96, 462-483, (2011) Mixed Hodge theory of singular varieties (complex-analytic aspects), Variation of Hodge structures (algebro-geometric aspects), Finite transformation groups Symmetric products of mixed Hodge modules
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Sklyanin algebras; elliptic \(R\)-matrices; self-adjoint representations; Hilbert space; irreducible representations Yu. N. Bespalov, ?Self-adjoint representations of Sklyanin algebras,? Ukr. Mat. Zh.,43, No. 11, 1567-1574 (1991). Quantum groups (quantized enveloping algebras) and related deformations, Nonassociative topological algebras with an involution, Elliptic curves, Representations of topological algebras with involution On selfadjoint representations of the Sklyanin algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Haraguchi, Yuki: On noncommutative extensions of ga by gm over an fp-algebra. Tsukuba J. Of math. 29, 405-435 (2005) Formal groups, \(p\)-divisible groups, Cohomology theory for linear algebraic groups On non-commutative extensions of \(G_a\) by \(G_m\) over an \(\mathbb F_p\)-algebra
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces formal deformations; 1-parameter deformations; algebra structures; associativity equation; automorphisms of modules; Hochschild cohomology; quadratic algebras; symplectic reflection algebras; deformations of representations P. Etingof, ``Exploring noncommutative algebras via deformation theory,'' math. QA/0506144. Deformations of associative rings, Formal methods and deformations in algebraic geometry, Noncommutative algebraic geometry Exploring noncommutative algebras via deformation theory.
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative two-tori; Fukaya category; holomorphic vector bundles A. Polishchuk and A. Schwarz. Categories of holomorphic vector bundles on noncommutative two-tori. \textit{Communications in Mathematical Physics}, (1)236 (2003), 135-159. arXiv:0211262v2 [math.QA] Noncommutative geometry (à la Connes), Global theory of symplectic and contact manifolds, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Calabi-Yau manifolds (algebro-geometric aspects), Holomorphic bundles and generalizations Categories of holomorphic vector bundles on noncommutative two-tori
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces number of rational points; homotopy type; Grassmann variety; Betti numbers; complex algebraic variety; mixed Hodge structure; weight filtration; Hodge filtration; invariant; weight polynomial; Euler characteristic Homotopy theory and fundamental groups in algebraic geometry, Rational points, Variation of Hodge structures (algebro-geometric aspects), Arithmetic ground fields (finite, local, global) and families or fibrations, Topological properties in algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Arithmetic varieties and schemes; Arakelov theory; heights, Transcendental methods, Hodge theory (algebro-geometric aspects) On the geometry of varieties of invertible symmetric and skew-symmetric matrices
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hasse-Schmidt derivation; integrable derivation; differential operator; substitution map; power divided algebra Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Commutative rings of differential operators and their modules, Derivations and commutative rings Rings of differential operators as enveloping algebras of Hasse-Schmidt derivations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces intersection cohomology; exotic symmetric space; nilpotent cone; Kostka polynomials; character sheaves T. Shoji, K. Sorlin, \textit{Exotic symmetric space over a finite field,} II, Transform. Groups \textbf{19} (2014), 887-926. Compactifications; symmetric and spherical varieties Exotic symmetric space over a finite field. II
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces slice of semisimple derivation; torus action; linearization Derivations and commutative rings, Group actions on varieties or schemes (quotients), Group actions on affine varieties A note on semisimple derivations of commutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces generic algebras; anticommutative algebras; finite dimensional algebras; Grassmannian; \(n\)-ary algebra; anticommutative algebraic geometry; \(D\)-regular algebras; \(E\)-regular algebras E. A. Tevelev, Subalgebras and discriminants of anticommutative algebras, Izv. Ross. Akad. Nauk Ser. Mat. 63 (1999), no. 3, 169 -- 184 (Russian, with Russian summary); English transl., Izv. Math. 63 (1999), no. 3, 583 -- 595. Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry, Exterior algebra, Grassmann algebras, Grassmannians, Schubert varieties, flag manifolds Subalgebras and discriminants of anticommutative algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric products; symmetric tensors; linear representations; moduli spaces; determinants; traces Group actions on varieties or schemes (quotients), Actions of groups on commutative rings; invariant theory, Representation theory for linear algebraic groups Symmetric products, linear representations and trace identities
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Ellenberg, J.S., Endomorphism algebras of Jacobians, Advances in Mathematics, 162, 243-271, (2001) Arithmetic ground fields for curves, Jacobians, Prym varieties, Abelian varieties of dimension \(> 1\), Arithmetic ground fields for abelian varieties, Coverings of curves, fundamental group Endomorphism algebras of Jacobians
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric functions; Springer representations; Kostka polynomials Group actions on varieties or schemes (quotients), Representation theory for linear algebraic groups, Hecke algebras and their representations, Representations of finite symmetric groups, Symmetric functions and generalizations, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Representations of Lie and linear algebraic groups over local fields Symmetric functions and Springer representations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces KdV hierarchy; intersection number; ramification integrals; Hain's theta class; Moyal torus Families, moduli of curves (algebraic), Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) Quadratic double ramification integrals and the noncommutative KdV hierarchy
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hasse-Schmidt derivation; exterior algebra; universal factorization algebra; Giambelli's formula; Bosonic and Fermionic representations by Date, Jimbo, Kashiwara and Miwa Grassmannians, Schubert varieties, flag manifolds, Classical problems, Schubert calculus Universal factorization algebras of polynomials represent Lie algebras of endomorphisms
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric matrices; commuting matrices; normal variety; singular locus of variety J. P. Brennan, On the normality of commuting varieties of symmetric matrices, Comm. Algebra 22 (1994), no. 15, 6409--6414. Commutativity of matrices, Matrices over function rings in one or more variables, Complete intersections, Lie algebras of linear algebraic groups On the normality of commuting varieties of symmetric matrices
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric differentials; quadrics; trisecant variety; low codimension Low codimension problems in algebraic geometry, Projective and enumerative algebraic geometry, Complete intersections Twisted symmetric differentials and the quadric algebra of subvarieties of \(\mathbb{P}^N\) of low codimension
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces signatures; Nullstellensatz; Positivstellensatz; Nichtnegativstellensatz; orderings; non-commutative rings DOI: 10.1016/S0022-4049(98)00067-X Relevant commutative algebra, Topological and ordered rings and modules, Noncommutative algebraic geometry, Ordered rings, algebras, modules Orderings of 2-power exponent on noncommutative rings
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces automorphisms; endomorphisms; linear coordinates; tame coordinates; polynomial algebras; Jacobian Polynomial rings and ideals; rings of integer-valued polynomials, Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem) Endomorphisms preserving coordinates of polynomial algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces formal groups; extension; Witt vector rings Formal groups, \(p\)-divisible groups, Cohomology theory for linear algebraic groups On non-commutative extensions of \(\widehat{\mathbf G}_a\) by \(\widehat{{\mathcal G}}^{(M)}\) over an \({\mathbb F}_p\)-algebra
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces operad; operad algebra; convexor; sphere Tronin, S. N., Algebras over operad of spheres, RussianMathematics (Iz. VUZ), 54, 63-71, (2010) Rational and birational maps Algebras over operad of spheres
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Discrete subgroups of Lie groups, Hyperbolic and Kobayashi hyperbolic manifolds, Character varieties, Invariants of 3-manifolds (including skein modules, character varieties), Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Differential geometry of symmetric spaces Toledo invariant of lattices in \(\mathrm{SU}(2,1)\) via symmetric square
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces elliptic algebra; Sklyanin algebra; twisted homogeneous coordinate ring; characteristic variety Noncommutative algebraic geometry, Sheaves in algebraic geometry, Rings arising from noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras) Maps from Feigin and Odesskii's elliptic algebras to twisted homogeneous coordinate rings
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative geometry; Riemann-Roch theorem; curved noncommutative torus; heat equation Khalkhali, M.; Moatadelro, A., A Riemann-Roch theorem for the noncommutative two torus, Journal of Geometry and Physics, 86, 19-30, (2014) Riemann-Roch theorems, Noncommutative algebraic geometry, Noncommutative differential geometry A Riemann-Roch theorem for the noncommutative two torus
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces cyclic algebra; Clifford algebra; invertible element; central simple dihedral \(F\)-algebra; root; conjugate splitting; Brauer group D. E. Haile, On dihedral algebras and conjugate splittings, in: Rings, Extensions, and Cohomology (Evanston, IL, 1993), Lecture Notes Pure Appl. Math., Vol. 159, Dekker, New York, 1994, pp. 107--111. Finite-dimensional division rings, Polynomials in real and complex fields: factorization, Skew fields, division rings, Brauer groups of schemes On dihedral algebras and conjugate splittings
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Infinite-dimensional Lie (super)algebras, Riemann surfaces; Weierstrass points; gap sequences, Cohomology of Lie (super)algebras, Lie algebras of vector fields and related (super) algebras, Differentials on Riemann surfaces Krichever-Novikov type algebras. An introduction
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative projective space; Koszul duality; Bernstein-Gel'fand-Gel'fand correspondence; graded Frobenius algebra; periodic injective resolution Jørgensen, P.: A noncommutative BGG correspondence, Pacific J. Math. 218, 357-377 (2005) Noncommutative algebraic geometry, Syzygies, resolutions, complexes in associative algebras, Graded rings and modules (associative rings and algebras) A noncommutative BGG correspondence
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Hopf algebra; quantum group; Drinfeld twist deformation; deformation quantization; universal enveloping algebra; bimodules; connection J. Wess, \textit{Deformed coordinate spaces: derivatives}, in \textit{Proceedings BW}2003 \textit{workshop, Vrnjacka Banja, Serbia and Montenegro}, G. Djordjevic, L. Nesic and J. Wess eds., World Scientific Singapore, (2005) [ISBN:9789812561305 (Print), 9789814481137 (Online)] [hep-th/0408080] [INSPIRE]. Local deformation theory, Artin approximation, etc., Bimodules in associative algebras, Drinfel'd modules; higher-dimensional motives, etc., Noncommutative algebraic geometry, Hopf algebras and their applications Noncommutative connections on bimodules and Drinfeld twist deformation
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine flag variety; affine quantum symmetric pair; canonical basis Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras, Quantum groups (quantized enveloping algebras) and related deformations, Linear algebraic groups over local fields and their integers, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Affine flag varieties and quantum symmetric pairs
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative topologies; quantales; sheaves Aguilar, J. Mendoza; Sánchez, M. V. Reyes; Verschoren, A.: Noncommutative topologies, localization and sheaves, Communications in algebra 36, 1289-1300 (2008) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Quantales, Noncommutative algebraic geometry, Presheaves and sheaves in general topology Noncommutative topologies, localization, and sheaves
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quantum affine \(\mathfrak{gl}_n\); coideal subalgebra; canonical basis; multiplication formula; affine flag variety; convolution algebra Quantum groups (quantized enveloping algebras) and related deformations, Linear algebraic groups over local fields and their integers, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Affine flag varieties and quantum symmetric pairs. II: Multiplication formula
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite-dimensional algebras; quaternions; algebraic \(K\)-theory; quadrics; \(K_ D\)-cycles \(K\)-theory of global fields, Quaternion and other division algebras: arithmetic, zeta functions, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Finite rings and finite-dimensional associative algebras, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Higher symbols, Milnor \(K\)-theory The group \(SK_ 2\) for quaternion algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite-dimensional algebras; quaternions; algebraic \(K\)-theory; quadrics; \(K^D\)-cycles --. --. --. --., The group \(SK_2\) for quaternion algebras (in Russian), Izv. Akad. Nauk SSSR Ser. Mat. 52 (1988), 310--335.; English translation in Math. USSR Izv. 32 (1989), 313--337. \(K\)-theory of global fields, Quaternion and other division algebras: arithmetic, zeta functions, Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Finite rings and finite-dimensional associative algebras, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Higher symbols, Milnor \(K\)-theory The group \(SK_ 2\) for quaternion algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces vertex operator algebra; mirror extension; conformal net; Knizhnik-Zamolodchikov equation Dong, C.; Jiao, X.; Xu, F., Mirror extensions of vertex operator algebras, Comm. Math. Phys., 329, 1, 263-294, (2014) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Vertex operators; vertex operator algebras and related structures, Pencils, nets, webs in algebraic geometry, Mirror symmetry (algebro-geometric aspects), Applications of Lie groups to the sciences; explicit representations, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Mirror extensions of vertex operator algebras
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Morphisms of commutative rings, Polynomial rings and ideals; rings of integer-valued polynomials, Rational and birational maps Automorphisms of polynomial algebras in \(2\) indeterminates over integral domains
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces equivariant compactification; symmetric varieties; character sheaves; finite groups of Lie type Semisimple Lie groups and their representations, Group varieties Compactifications of symmetric varieties and applications to representation theory
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Jordan norm similarities; symmetric determinants; affine group schemes; Jordan algebras Waterhouse, W. C.: Symmetric determinants and Jordan norm similarities in characteristic 2. Proc. amer. Math. soc. 93, No. 4, 583-589 (1985) Determinants, permanents, traces, other special matrix functions, Simple, semisimple Jordan algebras, Group schemes Symmetric determinants and Jordan norm similarities in characteristic 2
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Weyl algebras; irreducible modules; algebraic varieties; Bernstein filtrations; graded modules; finitely generated modules S. Coutinho. On involutive homogeneous varieties and representations of the Weyl algebra. J. of Algebra, 227 (2000), 195--210. Rings of differential operators (associative algebraic aspects), Filtered associative rings; filtrational and graded techniques, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Sheaves of differential operators and their modules, \(D\)-modules On involutive homogeneous varieties and representations of Weyl algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic topology; category theory; homological algebra; homotopy theory; operads Spectra with additional structure (\(E_\infty\), \(A_\infty\), ring spectra, etc.), Loop space machines and operads in algebraic topology, Operads (general), Topological categories, foundations of homotopy theory, Stable homotopy theory, spectra, Abstract and axiomatic homotopy theory in algebraic topology, Higher categories and homotopical algebra, Enriched categories (over closed or monoidal categories), Motivic cohomology; motivic homotopy theory, Homotopy theory and fundamental groups in algebraic geometry, Generalizations (algebraic spaces, stacks), Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) Symmetric operads in abstract symmetric spectra
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative algebraic variety; matrix polynomial algebra; deformations Noncommutative algebraic geometry, Formal methods and deformations in algebraic geometry Noncommutative algebraic varieties
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative convex polynomials; linear matrix inequalities D. M. Hay, J. W. Helton, A. Lim and S McCullough, Non-commutative partial matrix convexity, Indiana University Mathematics Journal 57 (2008), 2815--2842. Miscellaneous inequalities involving matrices, Linear operator inequalities, Semialgebraic sets and related spaces Non-commutative partial matrix convexity
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric bilinear forms on symmetric powers; orthogonal polynomials in several variables; homogeneous orthogonal polynomials; Gegenbauer polynomials; ultraspherical polynomials; Hermite polynomials; spherical harmonics; Hankel matrices; hyperkähler manifolds; irreducible holomorphically symplectic manifolds; Beauville-Bogomolov form; Beauville-Fujiki relation Parametrization (Chow and Hilbert schemes), Quadratic and bilinear forms, inner products, Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable, Kähler manifolds Symmetric powers of symmetric bilinear forms, homogeneous orthogonal polynomials on the sphere and an application to compact hyperkähler manifolds
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Borel orbits; reductive monoids; symmetric varieties Homogeneous spaces and generalizations, Representation theory for linear algebraic groups, Algebraic monoids Monoid embeddings of symmetric varieties
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces representations of quivers; non-commutative algebraic geometry; non-commutative curves Chan, D., Nyman, A.: Species and noncommutative \(\mathbb {P}^{1}\)'s over non-algebraic bimodules, in progress Representations of quivers and partially ordered sets, Noncommutative algebraic geometry Species and non-commutative \(\mathbb{P}^1\)'s over non-algebraic bimodules
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces nilpotent commutative algebra; smooth subvariety; annihilator G. Fels and W. Kaup, ''Nilpotent Algebras and Affinely Homogeneous Surfaces,'' Math. Ann. 353, 1315--1350 (2012). Hypersurfaces and algebraic geometry, Real submanifolds in complex manifolds Nilpotent algebras and affinely homogeneous surfaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric invariant; centralizer; polynomial algebra; Slodowy grading Charbonnel, J-Y; Moreau, A, The symmetric invariants of centralizers and slodowy grading, Math. Zeitschrift, 282, n\(\circle\) 1-2, 273-339, (2016) Simple, semisimple, reductive (super)algebras, Coadjoint orbits; nilpotent varieties, Geometric invariant theory The symmetric invariants of centralizers and Slodowy grading
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces weight structure; symmetric monoidal structure; stable infinity-categories Monoidal categories, symmetric monoidal categories, Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), \((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories The weight complex functor is symmetric monoidal
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Picard group; algebra over a non-algebraically closed field Class groups, Picard groups, Divisors, linear systems, invertible sheaves The Picard group of algebras over an algebraically nonclosed field
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Gromov width; Hofer-Zehnder capacity; complex Grassmannians; Cartan domains Loi, A., Mossa, R., Zuddas, F.: Symplectic capacities of Hermitian symmetric spaces of compact and non compact type. J. Sympl. Geom \textbf{12}(4) (2014) Gromov-Witten invariants, quantum cohomology, Frobenius manifolds, Differential geometry of symmetric spaces, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) Symplectic capacities of Hermitian symmetric spaces of compact and noncompact type
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces modular form; Brauer group; Gelbart-Jacquet adjoint lift Debargha Banerjee and Eknath Ghate, Adjoint lifts and modular endomorphism algebras, Israel J. Math. 195 (2013), no. 2, 507 -- 543. Brauer groups of schemes, Langlands-Weil conjectures, nonabelian class field theory, Abelian varieties of dimension \(> 1\), (Equivariant) Chow groups and rings; motives Adjoint lifts and modular endomorphism algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Riemannian symmetric space; invariant differential operators; Radon transform; space of horocycles; Plancherel formula; conical distributions; Fourier transform; harmonic functions S. Helgason, \textit{Geometric Analysis on Symmetric Spaces} (Am. Math. Soc., Providence, RI, 2008). Harmonic analysis on homogeneous spaces, Differential geometry of symmetric spaces, Harmonic maps, etc., Radon transform, Semisimple Lie groups and their representations, Analysis on real and complex Lie groups, Harmonic analysis and spherical functions, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Integral geometry, Positive definite functions on groups, semigroups, etc., Wave equation, Homogeneous spaces and generalizations Geometric analysis on symmetric spaces
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Heckman, J. J.; Verlinde, H., Covariant non-commutative space-time, \textit{Nuclear Physics. B. Theoretical, Phenomenological, and Experimental High Energy Physics. Quantum Field Theory and Statistical Systems}, 894, 58-74, (2015) Noncommutative geometry methods in quantum field theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Symmetry breaking in quantum theory, Quantum field theory on curved space or space-time backgrounds, Methods of noncommutative geometry in general relativity, Formal methods and deformations in algebraic geometry Covariant non-commutative space-time
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric spaces; quasisplit Hecke algebras; \(K\)-equivariant local systems; intersection cohomology Hecke algebras and their representations, Linear algebraic groups over finite fields, Grassmannians, Schubert varieties, flag manifolds, Group actions on varieties or schemes (quotients), Cohomology theory for linear algebraic groups Quasisplit Hecke algebras and symmetric spaces.
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces locally nilpotent derivation; equivariant embedding; linearization problem Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Derivations and commutative rings, Group actions on affine varieties, Affine fibrations Equivariant embeddings and semi-invariant locally nilpotent derivations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Fomin-Kirillov algebra; Coxeter group; nil-Coxeter algebra; Nichols algebra Jonah Blasiak, Ricky Ini Liu, Karola Mészáros, Subalgebras of the Fomin-Kirillov algebra. Preprint, 2012. arxiv:1310.4112. Reflection and Coxeter groups (group-theoretic aspects), Grassmannians, Schubert varieties, flag manifolds Subalgebras of the Fomin-Kirillov algebra
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces equivariant characteristic class; generating series formula; characteristic classes; orbifold classes; Hirzebruch- and Lefschetz-Riemann-Roch; external and symmetric products of varieties; representations of symmetric groups Maxim, L.; Schürmann, J., Cohomology representations of external and symmetric products of varieties Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Symmetric products and cyclic products in algebraic topology, Characteristic classes and numbers in differential topology, Representations of finite symmetric groups Equivariant characteristic classes of external and symmetric products of varieties
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces hyperbolic curve; outer Galois representation; injectivity; semi-graph of anabelioids; nodally nondegenerate; combinatorial anabelian geometry; combinatorial cuspidalization Klopsch, B.: An introduction to compact \(p\)-adic Lie groups. In: Lectures on Profinite Topics in Group Theory, vol.~77 of London Math. Soc. Stud. Texts, pp. 7-61. Cambridge University Press, Cambridge (2011) Coverings of curves, fundamental group, Families, moduli of curves (algebraic) On the combinatorial anabelian geometry of nodally nondegenerate outer representations
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces right commutative algebras; Novikov algebras; bicommutative algebras; nilpotent algebras; algebraic classification; central extension; geometric classification; degeneration Lie-admissible algebras, Nonassociative algebras satisfying other identities, Fibrations, degenerations in algebraic geometry, Group actions on varieties or schemes (quotients) The algebraic and geometric classification of nilpotent right commutative algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces graded rings; rings of differential operators; Ore localizations; Ore sets; quantum differential operators; quantum affine spaces; quantum enveloping algebras; Bernstein theorem; holonomic modules V.A. Lunts and A.L. Rosenberg, Differential operators on noncommutative rings, Selecta Math. (N.S.), 3 (1997), 335--359. Rings of differential operators (associative algebraic aspects), Ore rings, multiplicative sets, Ore localization, Graded rings and modules (associative rings and algebras), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Quantum groups (quantized enveloping algebras) and related deformations, Derivations, actions of Lie algebras, Sheaves of differential operators and their modules, \(D\)-modules Differential operators on noncommutative rings
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces weighted Bergman space; holomorphic covering map; the fundamental group; von Neumann algebra; type II factor H. Huang. von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory, Sci China Ser A, 2013, 56: 811--822. Linear operators in \(C^*\)- or von Neumann algebras, Coverings of curves, fundamental group, Classification of factors Von Neumann algebras generated by multiplication operators on the weighted Bergman space: a function-theory view into operator theory
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Painlevé equation; noncommutative geometry; noncommutative blowup; Hecke modification; Poisson structure; birational group action; quantum planes; Weyl group action E. M. Rains, Transformations of elliptic hypergeometric integrals , preprint,\arxivmath/0309252v4[math.QA] Noncommutative algebraic geometry, Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation), Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies Noncommutative geometry and Painlevé equations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces algebraic models of Nash sets; Nash sets with symmetries Real algebraic sets, Nash functions and manifolds, Topology of real algebraic varieties Algebraic models of symmetric Nash sets
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces multivariable operator theory; Berezin transform; noncommutative polydomain; noncommutative variety; free holomorphic function; Fock space; invariant subspace; dilation theory; characteristic function G. Popescu, Berezin transforms on noncommutative polydomains, preprint (2013), ; to appear in Trans. Amer. Math. Soc. Canonical models for contractions and nonselfadjoint linear operators, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Several-variable operator theory (spectral, Fredholm, etc.), Noncommutative algebraic geometry Berezin transforms on noncommutative varieties in polydomains
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces symmetric complex space in the sense of Borel; semisimple Lie; group; compact algebraic varieties Homogeneous complex manifolds, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Complex Lie groups, group actions on complex spaces, Homogeneous spaces and generalizations, Semisimple Lie groups and their representations On algebraic varieties that are symmetric in the sense of Borel
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces \(A_{\infty}\)-algebras; modular operads; homological perturbation; mirror symmetry; B-model; noncommutatative algebraic geometry; Feynman diagrams; ribbon graphs Barannikov, S., Solving the noncommutative Batalin-Vilkovisky equation, Lett. Math. Phys., 103, 6, 605-628, (2013) Supersymmetric field theories in quantum mechanics, Noncommutative geometry methods in quantum field theory, Noncommutative geometry in quantum theory, Feynman diagrams, Mirror symmetry (algebro-geometric aspects) Solving the noncommutative Batalin-Vilkovisky equation
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces factorization space; pullback by étale maps; factorization algebra; Ran space; D-module; Beilinson-Drinfeld Grassmannian; Hilbert scheme of points Brauer groups of schemes, Generalizations (algebraic spaces, stacks), \((\infty,1)\)-categories (quasi-categories, Segal spaces, etc.); \(\infty\)-topoi, stable \(\infty\)-categories, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Universal factorization spaces and algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative spaces; quantum groups; quantum field theory Noncommutative geometry methods in quantum field theory, Spinor and twistor methods applied to problems in quantum theory, Quantum groups and related algebraic methods applied to problems in quantum theory, Quantum groups (quantized enveloping algebras) and related deformations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Twisting, `finite' Poincaré transformations and QFT on noncommutative space
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces affine Lie algebras; central extensions; conformal field theory; genus zero Lie algebras; infinite dimensional Lie algebras; Krichever-Novikov type algebras Schlichenmaier, M, \(N\)-point Virasoro algebras are multipoint krichever-Novikov-type algebras, Commun. Algebra, 45, 776-821, (2017) Infinite-dimensional Lie (super)algebras, Riemann surfaces; Weierstrass points; gap sequences, Cohomology of Lie (super)algebras, Lie algebras of vector fields and related (super) algebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Virasoro and related algebras, Differentials on Riemann surfaces, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations \(N\)-point Virasoro algebras are multipoint Krichever-Novikov-type algebras
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces theory of invariants; Hilbert series; finite generatedness; freeness; asymptotics; noncommutative invariant theory of \(SL(2,\mathbb{C})\) Almkvist, Gert: Commutative and noncommutative invariant theory, Banach center publ. 26, 259-268 (1990) Representation theory for linear algebraic groups, Linear algebraic groups over the reals, the complexes, the quaternions, Vector and tensor algebra, theory of invariants, Trace rings and invariant theory (associative rings and algebras), Group actions on varieties or schemes (quotients) Commutative and noncommutative invariant theory
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Combinatorial representation theory; classical groups; Young tableaux; toric degenerations; flat algebras Sangjib Kim, Standard monomial theory for flag algebras of \?\?(\?) and \?\?(2\?), J. Algebra 320 (2008), no. 2, 534 -- 568. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Geometric invariant theory, Grassmannians, Schubert varieties, flag manifolds, Group actions on varieties or schemes (quotients) Standard monomial theory for flag algebras of GL\((n)\)and Sp\((2n)\)
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ring of formal series; Hopf algebras; quantum groups; coalgebra structure; m-valued formal group Kholodov, A. N.: Multi-dimensional two-valued commutative formal groups. J. soviet. Math. survey 43, 243-244 (1988) Formal groups, \(p\)-divisible groups Multidimensional two-valued commutative formal groups
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces ring of vector invariants; set of generators; Hilbert-Poincaré series H.E.A. Campbell, I. Hughes, and R.D. Pollack, \textit{Vector invariants of symmetric groups}, Canad. Math. Bull., 33 (1990), pp. 391--397. Geometric invariant theory, Subgroups of symmetric groups, Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Vector spaces, linear dependence, rank, lineability Vector invariants of symmetric groups
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Calogero phase spaces; coadjoint orbits; infinite dimensional Lie algebras; noncommutative symplectic geometry; varieties of representations; deformed preprojective algebras Bocklandt, R., Le Bruyn, L.: Necklace Lie algebras and noncommutative symplectic geometry. Math. Z. \textbf{240}, 141-167 (2002). arXiv:math/0010030 Representations of quivers and partially ordered sets, Infinite-dimensional Lie (super)algebras, Symplectic manifolds (general theory), Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry Necklace Lie algebras and noncommutative symplectic geometry.
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative matrices; strongly nilpotent matrices; Jacobian conjecture; tensor algebras DOI: 10.1080/03081089608818472 Canonical forms, reductions, classification, Automorphisms of curves, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) Noncommutative-nilpotent matrices and the Jacobian conjecture
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Lie algebras; invariant theory Panyushev, D.: \textit{Semi-direct products of Lie algebras, their invariants and representations}. Publ. Res. Inst. Math. Sci. \textbf{4}, 1199-1257 (2007) Group actions on varieties or schemes (quotients), Solvable, nilpotent (super)algebras, Semisimple Lie groups and their representations Semi-direct products of Lie algebras and their invariants
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