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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 compact Riemann surface; vector bundle of rank 2 Brambila, Algebras of endomorphisms of semistable vector bundles over a compact Riemann surface (1986) Families, moduli of curves (analytic), Compact Riemann surfaces and uniformization Endomorphisms algebras of semistable vector bundles
| 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 Hilbert-Chow morphism; divided Schemes and morphisms, Parametrization (Chow and Hilbert schemes), Representation theory of associative rings and algebras Moduli of linear representations, symmetric products and the non commutative Hilbert scheme
| 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 O. K, S., No article title, Dokl. Math., 89, 151-153, (2014) Infinite-dimensional Lie (super)algebras, Families, moduli of curves (algebraic), 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, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Lax operator algebras of type \(G_{2}\)
| 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 Saturation; generators; representability; triangulated categories A. Bondal & M. van den Bergh, ``Generators and representability of functors in commutative and noncommutative geometry'', Moscow Math. J.3 (2003) no. 1, p. 1-36, 258 Generators and representability of functors in commutative and noncommutative 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 geometry; spin networks; lattice gauge theory Marcolli, Matilde; van Suijlekom, Walter D., Gauge networks in noncommutative geometry, J. geom. phys., 75, 71-91, (2014) Noncommutative geometry methods in quantum field theory, Noncommutative global analysis, noncommutative residues, Noncommutative algebraic geometry Gauge networks in noncommutative 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 semisimple Lie algebra; commuting variety; Cartan subspace; quaternionic decomposition; nilpotent orbit; Jordan algebra Group actions on varieties or schemes (quotients), Coadjoint orbits; nilpotent varieties, Automorphisms, derivations, other operators for Lie algebras and super algebras, Simple, semisimple Jordan algebras, Semisimple Lie groups and their representations Commuting involutions of Lie algebras, commuting varieties, and simple Jordan 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 commutative algebra; Weyl algebra; commuting operators Mokhov, O. I., On commutative subalgebras of the Weyl algebra related to commuting operators of arbitrary rank and genus, Mat. Zametki, 94, 314-316, (2013) General theory of ordinary differential operators, Relationships between algebraic curves and integrable systems, Rings of differential operators (associative algebraic aspects) On commutative subalgebras of the Weyl algebra related to commuting operators of arbitrary rank and genus
| 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 Calabi-Yau manifolds; Frobenius algebras; Frobenius manifold structures Cao, H.-D., Zhou, J.: DGBV algebras and mirror symmetry. In: First International Congress of Chinese Mathematicians (Beijing, 1998), AMS/IP Studies in Advances Mathematics, vol. 20. American Mathematical Soceity, Providence, RI, pp. 279--289 (2001) Calabi-Yau manifolds (algebro-geometric aspects), Poisson manifolds; Poisson groupoids and algebroids, Gromov-Witten invariants, quantum cohomology, Frobenius manifolds DGBV algebras and mirror symmetry
| 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 arithmetic surfaces; fibers at infinity; spectral triples; \(L\)-factors; Schottky groups C. Consani and M. Marcolli, ''Noncommutative geometry, dynamics, and -adic Arakelov geometry,'' SelectaMath. (N.S.) 10(2), 167--231 (2004). Arithmetic varieties and schemes; Arakelov theory; heights, Noncommutative geometry (à la Connes), Noncommutative dynamical systems Noncommutative geometry, dynamics, and \(\infty\)-adic Arakelov 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 subalgebras of polynomial rings; quotients of the affine plane; rational vector field Polynomial rings and ideals; rings of integer-valued polynomials, Special surfaces, Modules of differentials Finitely generated algebras associated with rational vector fields
| 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 D-dimension Families, moduli, classification: algebraic theory Symmetric powers of vector bundles on 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 quantum algebras; Atiya-Drinfeld-Hitchin-Manin construction; instantons; noncommutative sphere S. Brain and G. Landi, ''Families of Monads and Instantons from a Noncommutative ADHM Construction,'' arXiv:0901.0772v1 [math.QA]. Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Yang-Mills and other gauge theories in quantum field theory, Noncommutative geometry in quantum theory Families of monads and instantons from a noncommutative ADHM construction
| 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 Proceedings, conferences, collections, etc. pertaining to commutative algebra, Theory of modules and ideals in commutative rings, Syzygies, resolutions, complexes and commutative rings, Singularities in algebraic geometry, Collections of articles of miscellaneous specific interest Commutative algebra and noncommutative algebraic geometry. Volume II: Research articles
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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 inversion problem; deformations of formal maps in noncommutative variables; inviscid Burgers-like equations; noncommutative inversion formulas Zhao, W.: Deformations and inversion formulas for formal maps in noncommutative variables Jacobian problem, Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables, KdV equations (Korteweg-de Vries equations) Deformations and inversion formulas for formal automorphisms in noncommutative variables
| 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 Brauer group; Azumaya R-algebras; smash products; Galois objects; dual Hopf R-algebras; groups of norm one units L.N. Childs, Non-isomorphic equivalent Azumaya algebras , Canad. Math. Bull. 30 (1987), 340-343. Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Units, groups of units (associative rings and algebras), Brauer groups of schemes, Finite rings and finite-dimensional associative algebras Non-isomorphic equivalent Azumaya 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 rational elliptic curves; Cuntz-Krieger algebras Noncommutative topology, Elliptic curves Noncommutative geometry of rational elliptic 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 DOI: 10.1142/S0217979200001953 Methods of noncommutative geometry in general relativity, Geometry of quantum groups, Noncommutative algebraic geometry Conceptual issues for noncommutative gravity on algebras and finite 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 root system; exterior algebra; Borel subalgebra Varieties and morphisms, Affine algebraic groups, hyperalgebra constructions, General properties and structure of other Lie groups, Semisimple Lie groups and their representations On some subspaces of the exterior algebra of a simple Lie 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 bicommutative algebras; nilpotent algebras; algebraic classification; central extension; geometric classification; degeneration Nonassociative algebras satisfying other identities, Fibrations, degenerations in algebraic geometry, Group actions on varieties or schemes (quotients) The algebraic and geometric classification of nilpotent bicommutative 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 compounded symmetric two-two correspondences Rational and birational maps, Projective analytic geometry, Ramification problems in algebraic geometry Commutativity of compounded symmetric two-two correspondences
| 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 derived categories; twisted forms; Hochschild cohomology; Brauer group Antieau, B.: Étale twists in noncommutative algebraic geometry and the twisted Brauer space Brauer groups of schemes, Algebraic moduli problems, moduli of vector bundles, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Noncommutative algebraic geometry Étale twists in noncommutative algebraic geometry and the twisted Brauer 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 Schur functions; Schubert polynomials; conjecture of Fomin and Kirillov; Grothendieck polynomial Lenart, C., Noncommutative Schubert calculus and Grothendieck polynomials.Adv. Math., 143 (1999), 159--183. Combinatorial aspects of representation theory, Grassmannians, Schubert varieties, flag manifolds Noncommutative Schubert calculus and Grothendieck polynomials
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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 real matrices; semisymplectic spaces Geometry of classical groups, Classical groups (algebro-geometric aspects), Linear algebraic groups over the reals, the complexes, the quaternions Semisymplectic spaces over the algebra of real 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 Grassmannian; noncommutative geometry; fiber bundles Grassmannians, Schubert varieties, flag manifolds, Noncommutative geometry (à la Connes) A short note on Grassmann manifolds with a view to noncommutative 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 branch points; symmetric two-two correspondences Ramification problems in algebraic geometry, Rational and birational maps Commutativity of irreducible symmetric two-two correspondences which have the same branch 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 Classical groups (algebro-geometric aspects), Symmetric functions and generalizations, Positive characteristic ground fields in algebraic geometry, Reflection and Coxeter groups (group-theoretic aspects) Character sheaves on exotic symmetric spaces and Kostka polynomials
| 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 Sethuraman, B. A., The algebra generated by three commuting matrices, Math. Newsl., 21, 2, 62-67, (2011) Endomorphism rings; matrix rings, Algebraic systems of matrices, Determinantal varieties The algebra generated by three commuting 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 quantum statistical model; \(C^*\)-dynamical system; commensurable class of \(Q\)-lattice; KMS state; Type \(\text{II}_1\)-factor; modular field; Eisenstein series A. Connes and M. Marcolli, ''From physics to number theory via noncommutative geometry. Part I: Quantum statistical mechanics of Q-lattices,'' in Frontiers in Number Theory, Physics, and Geometry, I pp. 269--350 (Springer Verlag, 2006). Noncommutative geometry (à la Connes), Quantum dynamics and nonequilibrium statistical mechanics (general), Noncommutative geometry in quantum theory, Other ``noncommutative'' mathematics based on \(C^*\)-algebra theory, Arithmetic problems in algebraic geometry; Diophantine geometry, Relations with noncommutative geometry From physics to number theory via noncommutative geometry
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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 Azumaya algebra; Brauer group; singular set; function field DeMeyer, F. R., Ford, T. J. (1992). Nontrivial, locally trivial Azumaya algebras. In:Azumaya Algebras, Actions, and Modules (Bloomington, IN, 1990). Contemporary Mathematics, Vol. 124. Providence, RI: American Mathematical Society, pp. 39--49 [MR 1144027 (93a:13001)]. Brauer groups of schemes, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Étale and other Grothendieck topologies and (co)homologies, Singularities of surfaces or higher-dimensional varieties Nontrivial, locally trivial Azumaya 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 isolated singularity; moduli algebra; Milnor number; Brieskorn-Pham singularity; Kouchnirenko's formula 149 A. Elashvili, M. Jibladze, and È.~B. Vinberg, \emph Moduli algebras of some simplest non-semiquasihomogeneous singularities, Funct. Anal. Appl., \textbf 51:2 (2017), Algebraic moduli problems, moduli of vector bundles, Singularities in algebraic geometry Moduli algebras of some non-semiquasihomogeneous singularities
| 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 vertex operator algebra; semi-infinite Plücker-type relations; homogeneous coordinate ring Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Vertex operators; vertex operator algebras and related structures, Grassmannians, Schubert varieties, flag manifolds Vertex algebras and coordinate rings of semi-infinite flags
| 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 Noetherian graded rings; noncommutative projective geometry; idealizer rings; strongly left Noetherian algebras Rogalski, D.: Idealizer rings and noncommutative projective geometry. J. algebra 279, 791-809 (2004) Rings arising from noncommutative algebraic geometry, Graded rings and modules (associative rings and algebras), Noetherian rings and modules (associative rings and algebras), Module categories in associative algebras, Homological functors on modules (Tor, Ext, etc.) in associative algebras, Noncommutative algebraic geometry, Projective techniques in algebraic geometry Idealizer rings and noncommutative projective geometry
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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 semiprime graded algebras; Noetherian rings; Gelfand-Kirillov dimension; twisted homogeneous coordinate rings; Veronese rings; noncommutative projective geometry; noncommutative projective curves; algebras of quadratic growth Artin, M.; Stafford, J. T., Semiprime graded algebras of dimension two, J. Algebra, 227, 1, 68-123, (2000) Graded rings and modules (associative rings and algebras), Noetherian rings and modules (associative rings and algebras), Growth rate, Gelfand-Kirillov dimension, Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Finite rings and finite-dimensional associative algebras Semiprime graded algebras of dimension two
| 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 multiplicity free representation; admissible representation; visible action; (real) spherical variety; Hermitian symmetric space; tube type domain Semisimple Lie groups and their representations, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Homogeneous spaces and generalizations Admissible representations, multiplicity-free representations and visible actions on non-tube type Hermitian 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 polynomial mappings; blue indeterminates; white indeterminates; signal R. Peretz, Constructing Polynomial Mappings Using Non-commutative Algebras. In Aff. Algebr. Geometry. Contemporary Mathematics, vol. 369 (American Mathematical Society, Providence, 2005), pp. 197-232 Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Noncommutative algebraic geometry Constructing polynomial mappings using non-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 Representations of quivers and partially ordered sets, Noncommutative algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects) Nonnoetherian homotopy dimer algebras and noncommutative crepant resolutions
| 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 smooth manifolds; smooth manifolds with symmetries; affine Nash manifolds; nonsingular real algebraic sets Nash functions and manifolds, Real algebraic sets, Topology of real algebraic varieties On the algebraic models of symmetric smooth 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 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Fourier coefficients of automorphic forms, \(K3\) surfaces and Enriques surfaces, Relationships between surfaces, higher-dimensional varieties, and physics Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections
| 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 \( \tau \)-tilting theory; minimal representation infinite algebra; brick; non-distributive lattices; representation varieties; Brauer-thrall conjectures; minimal \(\tau \)-tilting infinite algebra Representations of quivers and partially ordered sets, Representation type (finite, tame, wild, etc.) of associative algebras, Combinatorial aspects of representation theory, Algebraic moduli of abelian varieties, classification \(\tau\)-tilting finiteness of non-distributive algebras and their module 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-associative algebras; problem of Albert; invariant bilinear forms; nil-algebras; solvable algebras; polynomial endomorphisms; Jacobian conjecture Power-associative rings, Structure theory for nonassociative algebras, Automorphisms, derivations, other operators (nonassociative rings and algebras), Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem), Jacobian problem The space of invariant bilinear forms of the polarization algebra of a polynomial endomorphism: an approach to the problem of Albert
| 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 entanglement; Bell state; nonlocality; emergence; non-Noetherian ring; matrix factorization; noncommutative blowup; quantum foundations; quantum information; noncommutative algebraic geometry 5. C. Beil, The Bell states in noncommutative algebraic geometry, to appear in Int. J. Quantum Inform. Quantum coherence, entanglement, quantum correlations, Noncommutative geometry in quantum theory, Noncommutative algebraic geometry The Bell states in noncommutative algebraic geometry
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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 étale quadratic extension; Brauer group; Azumaya S-algebra; involutions; Brauer equivalent Knus, M. -A.; Parimala, R.; Srinivas, V.: Azumaya algebras with involutions. J. algebra 130, 65-82 (1990) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Rings with involution; Lie, Jordan and other nonassociative structures, Centralizing and normalizing extensions, Brauer groups of schemes Azumaya algebras with involutions
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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 DGcat; Qcoh\((X)\); nocommutative motives; differential graded algebras Noncommutative algebraic geometry Noncommutative geometry in the framework of differential graded categories
| 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 space; arithmetic variety; Kuga fiber variety Modular and Shimura varieties, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Homogeneous spaces and generalizations Conjugates of \((H_ 2)\)-equivariant maps of symmetric 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 Brauer groups; elementary symmetric polynomial Brauer groups of schemes, Brauer groups (algebraic aspects) Division algebras that ramify only on the zeros of an elementary symmetric polynomial
| 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 semisimple Lie algebra; Cartan decomposition; nilpotent orbit; Slodowy slice; sheet; Jordan class Bulois, M, Sheets of symmetric Lie algebras and slodowy slices, J. Lie Theory, 21, 1-54, (2011) Group actions on varieties or schemes (quotients), Simple, semisimple, reductive (super)algebras, Semisimple Lie groups and their representations Sheets of symmetric Lie algebras and Slodowy slices
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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 algebra of hypersurface; Micali chain of ideals Ideals and multiplicative ideal theory in commutative rings, Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal), Commutative rings and modules of finite generation or presentation; number of generators, Relevant commutative algebra Algèbres symétriques et singularités. (Symmetric algebras and singularities)
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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 algebra; singularity of hypersurface Polynomial rings and ideals; rings of integer-valued polynomials, Homological methods in commutative ring theory, Structure, classification theorems for modules and ideals in commutative rings, Singularities in algebraic geometry Algèbres symétriques et singularités. (Symmetric algebras and singularities)
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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-angled Artin groups; partially commutative groups; outer automorphism groups; BNS invariants; Bieri-Neumann-Strebel invariants; subspace arrangements; homology theory Geometric group theory, Other groups related to topology or analysis, Configurations and arrangements of linear subspaces, Braid groups; Artin groups Subspace arrangements, BNS invariants, and pure symmetric outer automorphisms of right-angled Artin 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 noncommutative polynomial; factorization; singularity locus; linear matrix inequality; spectrahedron; invariant theory Trace rings and invariant theory (associative rings and algebras), Ordinary and skew polynomial rings and semigroup rings, Real algebra, Semialgebraic sets and related spaces, Divisibility, noncommutative UFDs Geometry of free loci and factorization of noncommutative polynomials
| 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 arithmetic spaces; functor of points; Arakelov height; arithmetic curves Arithmetic varieties and schemes; Arakelov theory; heights, Noncommutative algebraic geometry Functor of points and height functions for noncommutative Arakelov geometry
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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 homogeneous Poisson-commutative subalgebras; Mishchenko-Fomenko algebras; Gelfand-Tsetlin algebra; symmetric algebra of reductive Lie algebras; completeness on co-adjoint orbits; nilpotent orbits; integrable systems; moment map; coisotropic actions Poisson algebras, Group actions on varieties or schemes (quotients), Coadjoint orbits; nilpotent varieties, Simple, semisimple, reductive (super)algebras, Semisimple Lie groups and their representations Poisson-commutative subalgebras and complete integrability on non-regular coadjoint orbits and flag 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 Infinite-dimensional Lie (super)algebras, Families, moduli of curves (algebraic), 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, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics Lax operator algebras of type \(G_2\)
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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 noncommutative algebraic geometry; bivariant cyclic cohomology; Connes' bilinear pairings; noncommutative motives \(K\)-theory and homology; cyclic homology and cohomology, Motivic cohomology; motivic homotopy theory, Negative \(K\)-theory, NK and Nil Bivariant cyclic cohomology and Connes' bilinear pairings in noncommutative motives
| 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 Hopf algebra of motivic integrals; motivic multiple polylogarithm Hopf algebra; motivic fundamental groupoids; noncommutative geometry; Feynman integrals A.B. Goncharov, \textit{Galois symmetries of fundamental groupoids and noncommutative geometry}, \textit{Duke Math. J.}\textbf{128} (2005) 209 [math.AG/0208144] [INSPIRE]. Polylogarithms and relations with \(K\)-theory, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Galois theory, Transcendental methods, Hodge theory (algebro-geometric aspects), Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Quantum groups and related algebraic methods applied to problems in quantum theory, Fundamental groups and their automorphisms (group-theoretic aspects) Galois symmetries of fundamental groupoids and noncommutative 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 completely reducible modules; connected semi-simple algebraic group; parabolic subgroup; representation; external tensor product; vector bundles Representation theory for linear algebraic groups, Cohomology theory for linear algebraic groups, Homogeneous spaces and generalizations, Classical groups (algebro-geometric aspects) Symmetric and exterior powers of homogeneous vector bundles
| 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 Chow ring; homogeneous spaces Field, R., The Chow ring of the symmetric space \textit{gl}(\textit{2n},\(\mathbb{C}\))/\textit{SO}(\textit{2n},\(\mathbb{C}\)), J. of Algebra, 349, 364-371, (2012) Algebraic cycles, Supervarieties The Chow ring of the symmetric space \(\mathrm{GL}(2n,\mathbb C)/\mathrm{SO}(2n,\mathbb C)\)
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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 Gelfand-Kirillov dimension; flag varieties; Hopf algebras; semisimple algebraic groups; quantum algebras; induced modules; graded algebras; induced representations Growth rate, Gelfand-Kirillov dimension, Graded rings and modules (associative rings and algebras), Representation theory for linear algebraic groups, Classical groups (algebro-geometric aspects) The Gelfand-Kirillov dimensions of algebras arising from representation 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 prehomogeneous vector space; representation; Young diagram; invariant Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Vector and tensor algebra, theory of invariants, Representation theory for linear algebraic groups, Prehomogeneous vector spaces Relative invariants of 2-simple prehomogeneous vector spaces of type I
| 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 normal form; rational invariant; tensorial representation; traceless tensor; two-dimensional vector space; Zariski-open subset Mu\(###\)noz Masqué, J.; Rosado Mara, M. E., Rational invariants on the space of all structures of algebras on a two-dimensional vector space, Electron. J. Linear Algebra, 23, 483-507, (2012) Vector and tensor algebra, theory of invariants, Canonical forms, reductions, classification, Geometric invariant theory, Classical groups (algebro-geometric aspects) Rational invariants on the space of all stuctures of algebras on a two-dimensional vector space
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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 Stetsko, M. M., Dirac oscillator and nonrelativistic snyder-de Sitter algebra, \textit{Journal of Mathematical Physics}, 56, 1, (2015) Selfadjoint operator theory in quantum theory, including spectral analysis, Supersymmetry and quantum mechanics, Commutation relations and statistics as related to quantum mechanics (general), Formal methods and deformations in algebraic geometry Dirac oscillator and nonrelativistic Snyder-de Sitter 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 symmetric space; homogeneous space; real structure; real form Compactifications; symmetric and spherical varieties, Homogeneous spaces and generalizations, Linear algebraic groups over the reals, the complexes, the quaternions, Galois cohomology of linear algebraic groups, Real algebraic and real-analytic geometry Real structures 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 Lie coalgebras; universal coenveloping algebras; bialgebras; Poincaré- Birkhoff-Witt theorem; filtered universal enveloping coalgebra; Milnor- Moore-André theorem Block, R E, Commutative Hopf algebras, Lie coalgebras, and divided powers, J Algebra, 96, 275-306, (1985) Universal enveloping (super)algebras, Graded Lie (super)algebras, Affine algebraic groups, hyperalgebra constructions Commutative Hopf algebras, Lie coalgebras, and divided powers
| 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 infinite dimensional Lie algebras, current algebras, gauge algebras, Kac-Moody algebras; Krichever-Novikov algebras; affine algebras; central extensions; fermionic representations; wedge representations; highest weight modules O. K. Sheinman, ''Krichever-Novikov Algebras, Their Representations and Applications,'' in Geometry, Topology, and Mathematical Physics. S. P. Novikov's Seminar 2002--2003, Ed. by V.M. Buchstaber and I.M. Krichever (Am. Math. Soc., Providence, R.I., 2004), pp. 297--316. Infinite-dimensional Lie (super)algebras, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Virasoro and related algebras, Loop groups and related constructions, group-theoretic treatment, Vector bundles on curves and their moduli, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Riemann-Hilbert problems in context of PDEs, Riemann surfaces; Weierstrass points; gap sequences Affine Krichever-Novikov algebras, their representations and applications
| 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 Witt vectors' noncommutative rings Noncommutative algebraic geometry, Witt vectors and related rings The rings of Witt vectors for noncommutative rings with some rich structure
| 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; general linear groups; symmetric groups; infinitesimal Schur algebras; finite representation type; indecomposable modules; polynomial representations; group schemes; Frobenius endomorphisms Doty, S; Nakano, D; Peters, K, Infinitesimal Schur algebras of finite representation type, Quart. J. Math., 48, 323-345, (1997) Representation theory for linear algebraic groups, Representations of finite symmetric groups, Representation type (finite, tame, wild, etc.) of associative algebras, Group schemes Infinitesimal Schur algebras of finite representation type
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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 algebras; representations of the Witt algebra; symmetric polynomials; symmetric powers of curves; commuting operators; polynomial dynamical systems Lie algebras of vector fields and related (super) algebras, Applications of Lie algebras and superalgebras to integrable systems, Families, moduli of curves (algebraic), Plane and space curves, Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures Infinite-dimensional Lie algebras determined by the space of symmetric squares of hyperelliptic 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 Configurations and arrangements of linear subspaces, Hecke algebras and their representations, Reflection and Coxeter groups (group-theoretic aspects), Connections of hypergeometric functions with groups and algebras, and related topics Subspace arrangements and Cherednik 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 Homological Mirror Symmetry; Weighted Projective Planes; Noncommutative deformations; Lagrangian Vanishing Cycles; Fano Manifolds; Hirzebruch Surfaces; Derived Categories Auroux D, Katzarkov L, Orlov D. Mirror symmetry for weighted projective planes and their noncommutative deformations. Ann of Math (2), 2008, 167: 867--943 Mirror symmetry (algebro-geometric aspects), Noncommutative algebraic geometry, Symplectic aspects of Floer homology and cohomology Mirror symmetry for weighted projective planes and their noncommutative deformations
| 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 Simple, semisimple, reductive (super)algebras, Coadjoint orbits; nilpotent varieties, Actions of groups on commutative rings; invariant theory, Geometric invariant theory The symmetric invariants of centralizers and Slodowy grading. 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 double derivations; double Schouten bracket; double Poisson bracket; quivers; double Poisson algebras G. Van de Weyer, Double Poisson structures on finite dimensional semi-simple algebras, math.AG/0603533. Noncommutative algebraic geometry Double Poisson structures on finite dimensional semi-simple 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 Maeda Y, Sako A. Noncommutative deformation of spinor zero mode and ADHM construction. J Math Phys, 2012, 53: 022303 Geometry and quantization, symplectic methods, Deformation quantization, star products, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics, Noncommutative geometry in quantum theory, Green's functions for elliptic equations Noncommutative deformation of spinor zero mode and Atiyah-Drinfeld-Hitchin-Manin construction
| 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 bialgebras; Stanley symmetric functions; Coxeter groups; permutations; combinatorial coalgebras Symmetric functions and generalizations, Combinatorial aspects of algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Hopf algebras and their applications, Reflection and Coxeter groups (group-theoretic aspects) Bialgebras for Stanley symmetric functions
| 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 algebras; actions of finite dimensional cocommutative Hopf algebras; Noether's theorem; finite groups of automorphisms; triangular Hopf algebras; quantum-commutative modules; non-commutative determinant functions; symmetric braidings; twist maps; categories of modules; Grassmann algebras; group gradings Cohen, M.; Westreich, S.; Zhu, S., Determinants, integrality and Noether's theorem for quantum commutative algebras, Israel J. math., 96, 185-222, (1996) Automorphisms and endomorphisms, Geometric invariant theory, Determinants, permanents, traces, other special matrix functions Determinants, integrality and Noether's theorem for quantum 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 Zamolodchikov tetrahedron equation; birational maps; non-abelian Hirota-Miwa system; Desargues lattices; Weyl commutation relations Lattice dynamics; integrable lattice equations, Integrable difference and lattice equations; integrability tests, Rational and birational maps, Yang-Baxter equations, Groups and algebras in quantum theory and relations with integrable systems Non-commutative birational maps satisfying Zamolodchikov equation, and Desargues lattices
| 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 V.\ M. Buchstaber and N. Ray, Flag manifolds and the Landweber-Novikov algebra, Geom. Topol.\textbf{2} (1998), 79-101. Complex cobordism (\(\mathrm{U}\)- and \(\mathrm{SU}\)-cobordism), Grassmannians, Schubert varieties, flag manifolds, Toric varieties, Newton polyhedra, Okounkov bodies Flag manifolds and the Landweber-Novikov 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 Hermitian symmetric spaces; multiplicity free actions; Littlewood--Richardon coefficients; Jack polynomials Group actions on varieties or schemes (quotients), Semisimple Lie groups and their representations Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients
| 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 monoid; group embedding; grading; locally nilpotent derivation; local algebra; toric variety; Cox ring; Demazure root; additive action Group actions on affine varieties, Commutative semigroups, Algebraic monoids, Linear algebraic groups over arbitrary fields Commutative algebraic monoid structures on affine spaces
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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 Bykov, D., Integrable properties of \(\sigma\)-models with non-symmetric target spaces, Nucl. Phys. B, 894, 254-267, (2015) Model quantum field theories, Groups and algebras in quantum theory and relations with integrable systems, Grassmannians, Schubert varieties, flag manifolds Integrable properties of \(\sigma\) -models with non-symmetric target spaces
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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 multiplicity; determinantal ideal; extended Hankel matrix Linkage, complete intersections and determinantal ideals, Determinantal varieties Multiplicity of algebras of minors of extended Hankel 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 Rogalski, D., Noncommutative projective geometry, Noncommutative algebraic geometry, 13-70, (2016), Cambridge University Press: Cambridge University Press, New York Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry Noncommutative projective geometry
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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 noetherian graded rings; twisted homogeneous coordinate rings J. T. Stafford, ''Noncommutative projective geometry,'' in: Proceedings of the International Congress of Mathematicians, Vol. II, Beijing (2002), Higher Ed. Press, Beijing (2002), pp. 93--103. Noncommutative algebraic geometry, Rings arising from noncommutative algebraic geometry Noncommutative projective geometry
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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 spaces; locally symmetric spaces; locally mixed symmetric spaces; Kuga fiber spaces; elliptic surfaces Research exposition (monographs, survey articles) pertaining to differential geometry, Research exposition (monographs, survey articles) pertaining to topological groups, Research exposition (monographs, survey articles) pertaining to algebraic topology, Differential geometry of symmetric spaces, Local differential geometry of Hermitian and Kählerian structures, Global differential geometry of Hermitian and Kählerian manifolds, Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects), Special surfaces, Elliptic surfaces, elliptic or Calabi-Yau fibrations, Homogeneous spaces, Fiber spaces in algebraic topology, Discrete subgroups of Lie groups Locally mixed symmetric spaces
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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 double Poisson algebras; A-infinity algebra; pre-Calabi-Yau algebras; double P-infty algebra Differential graded algebras and applications (associative algebraic aspects), Noncommutative algebraic geometry, Poisson algebras, Bar and cobar constructions Cyclic \(A_\infty\)-algebras and double Poisson 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 root system of type \(A\); equivariant Pieri rule; Nichols-Woronowicz algebra Kirillov, A. N. and Maeno, T., Extended quadratic algebra and a model of the equivariant cohomology ring of flag varieties, St. Petersburg Math. J., 22, 3, 447-462, (2011) Grassmannians, Schubert varieties, flag manifolds Extended quadratic algebra and a model of the equivariant cohomology ring of flag 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 symmetric Leibniz algebra; weakly associative algebra; nilpotent algebra; isomorphism class; affine variety; orbit; open orbit; irreducible component; dimension; degenerate; Grunewald-O'Halloran conjecture; rigid; Vergne conjecture Nonassociative algebras satisfying other identities, Leibniz algebras, Fibrations, degenerations in algebraic geometry, Group actions on varieties or schemes (quotients) The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz 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 \(G\)-scheme; 2-cocycle; semidirect product algebra; twisted group algebra; equivariant algebraic \(K\)-theory; twisted projective homogeneous scheme; full exceptional collection; equivariant motivic measure; noncommutative algebraic geometry; \(G\)-equivariant Chow motive; \(G\)-equivariant perfect complex; noncommutative Chow motives Noncommutative algebraic geometry, Group actions on varieties or schemes (quotients), Twisted and skew group rings, crossed products, Equivariant \(K\)-theory, Orbifold cohomology Equivariant noncommutative motives
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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 commensurability of \(\mathbb{Q}\)-lattices; congruence subgroups Representation-theoretic methods; automorphic representations over local and global fields, Structure of modular groups and generalizations; arithmetic groups, Noncommutative algebraic geometry Noncommutative geometry of groups like \(\Gamma_0(N)\)
| 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 extended space; homogeneous complex manifold; transitive group of analytic automorphisms; hypercircle; group of motions; classical symmetric domains; non-symmetric classical domains Homogeneous complex manifolds, Homogeneous spaces and generalizations Extended spaces of non-symmetric classical 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 noncommutative theta functions; noncommutative torus DOI: 10.1023/A:1021272314232 Noncommutative geometry (à la Connes), Theta functions and abelian varieties Differential and complex geometry of two-dimensional noncommutative 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 elliptic curve; noncommutative torus D'Andrea, Francesco and Fiore, Gaetano and Franco, Davide, Modules over the noncommutative torus and elliptic curves, Letters in Mathematical Physics, 104, 11, 1425-1443, (2014) Noncommutative topology, Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables), Families, moduli of curves (analytic) Modules over the noncommutative torus and elliptic curves
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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 group actions; Hochschild cohomology; formal deformations; equivariant cohomology (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.), Deformations and infinitesimal methods in commutative ring theory, Formal methods and deformations in algebraic geometry, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Finite groups of transformations in algebraic topology (including Smith theory), Equivariant homology and cohomology in algebraic topology Equivariant one-parameter deformations of associative 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 Koszul algebras; quiver; homogeneous variety Hille L.: Homogeneous vector bundles and Koszul algebras. Math. Nach. 191, 189--195 (1998) Grassmannians, Schubert varieties, flag manifolds, Representations of quivers and partially ordered sets, Linear algebraic groups over arbitrary fields Homogeneous vector bundles and Koszul 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 free semialgebraic set; free invertibility set; free spectrahedron; linear matrix inequality; semidefinite programming Semialgebraic sets and related spaces, Matrix pencils, Convex sets without dimension restrictions (aspects of convex geometry), Rings with involution; Lie, Jordan and other nonassociative structures, Infinite-dimensional and general division rings, Semidefinite programming Noncommutative polynomials describing convex 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 noncommutative projective three-spaces; Koszul Calabi-Yau algebra Quadratic and Koszul algebras, Yang-Baxter equations, Noncommutative algebraic geometry Calabi-Yau property of noncommutative projective three-spaces and quantum Yang-Baxter 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 noncommutative geometry; Riemann zeta function [C]A. Connes, Noncommutative geometry and the Riemann zeta function, in: Mathematics: Frontiers and Perspectives, V. Arnold et al. (eds.), Amer. Math. Soc., 2000, 35--54. Nonreal zeros of \(\zeta (s)\) and \(L(s, \chi)\); Riemann and other hypotheses, Research exposition (monographs, survey articles) pertaining to number theory, History of number theory, Noncommutative differential geometry, Class field theory, Symmetry breaking in quantum theory, Class field theory; \(p\)-adic formal groups, \(\zeta (s)\) and \(L(s, \chi)\), Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas), Noncommutative geometry (à la Connes), Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Spectral problems; spectral geometry; scattering theory on manifolds Noncommutative geometry and the Riemann zeta function
| 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 del Pezzo surfaces; Poisson structures; Calabi-Yau deformations; Hochschild cohomology Etingof, P., Ginzburg, V.: Noncommutative del Pezzo surfaces and Calabi--Yau algebras. arXiv:0709.3593 Deformations of singularities, Elliptic curves, Calabi-Yau manifolds (algebro-geometric aspects), Cohen-Macaulay modules Noncommutative del Pezzo surfaces and Calabi-Yau 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 coinvariant elements; cotensor product; right \(H\)-comodule algebras; right \(H\)-module coalgebras; Hopf modules; normal basis theorem; Hopf algebras; affine algebraic group schemes Schneider, Hans-Jürgen, Principal homogeneous spaces for arbitrary Hopf algebras, Israel J. Math., 72, 1-2, 167-195, (1990) Group schemes Principal homogeneous spaces for arbitrary Hopf 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 Apéry monomial; Cohen-Macaulay; complete intersection; Gorenstein; numerical semigroup; numerical semigroup algebra Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.), Singularities of curves, local rings, Commutative semigroups, Semigroup rings, multiplicative semigroups of rings Numerical semigroup 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 Ruth I. Michler, Gröbner bases of symmetric quotients and applications, Algebra, arithmetic and geometry with applications (West Lafayette, IN, 2000) Springer, Berlin, 2004, pp. 627 -- 637. Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Singularities of surfaces or higher-dimensional varieties, Computational aspects of algebraic surfaces Gröbner bases of symmetric quotients and applications
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