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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 algebraic geometry Kuga, M.: Fiber Varieties Over a Symmetric Space Whose Fibers are Abelian Varieties, vol. I. University of Chicago, Chicago (1963-1964) Algebraic geometry Fiber varieties over a symmetric space whose fibers are abelian 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 AGT correspondence; Macdonald symmetric function; Ding-Iohara-Miki algebra; singular vector Quantum groups and related algebraic methods applied to problems in quantum theory, Quantum groups (quantized enveloping algebras) and related deformations, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Formal methods and deformations in algebraic geometry, Yang-Mills and other gauge theories in quantum field theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, String and superstring theories; other extended objects (e.g., branes) in quantum field theory Singular vectors of the Ding-Iohara-Miki 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 Hopf dg algebra; weak Tannakian formalism; Hochschild homology; algebraic \(K\)-theory; mixed Artin-Tate motives; orbit category; noncommutative algebraic geometry ______, {\em Noncommutative mixed (Artin) motives and their motivic Hopf dg algebras}. Selecta Mathematica, \textbf{22} (2016), no.~2, 735--764 Noncommutative algebraic geometry, (Equivariant) Chow groups and rings; motives, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Hopf algebras and their applications, \(K\)-theory and homology; cyclic homology and cohomology Noncommutative mixed (Artin) motives and their motivic Hopf dg 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 vertex operator algebras; Jacobi identity; contragredient modules; vertex operator map; moonshine module; intertwining operators; fusion rules; Verlinde algebras; moduli space of multipunctured Riemann spheres; conformal field theory Huang, Y. -Z.: Introduction to vertex operator algebras, III. Moonshine and vertex operator algebras, 51-77 (1995) Vertex operators; vertex operator algebras and related structures, Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras, Simple groups: sporadic groups, Virasoro and related algebras, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Algebraic moduli problems, moduli of vector bundles Introduction to vertex operator algebras. III
| 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 regular prehomogeneous vector spaces; characteristic 2 Chen, Z, A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic 2, Acta Math. Sinica, 2, 168-177, (1986) Homogeneous spaces and generalizations, Linear algebraic groups over arbitrary fields A classification of irreducible prehomogeneous vector spaces over an algebraically closed field of characteristic 2. 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 rigid geometry, Berkovich spaces; analytification; algebraic spaces; étale quotient Alper, J., Hall, J., Rydh, D.: A Luna étale slice theorem for algebraic stacks. (Preprint). arXiv:1504.06467 Rigid analytic geometry, Generalizations (algebraic spaces, stacks), Group actions on varieties or schemes (quotients) Non-archimedean analytification of algebraic 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 Hilbert series of a graded algebra; complete intersection Fröberg, R.; Löfwall, C., On Hilbert series for commutative and noncommutative graded algebras, J. Pure Appl. Algebra, 76, 33-38, (1990) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series, Graded rings and modules (associative rings and algebras), Graded rings, Complete intersections, Linkage, complete intersections and determinantal ideals On Hilbert series for commutative and noncommutative graded 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 height functions Valerio Talamanca, Height-preserving transformations on linear spaces, Ph. D. Thesis, Brandeis University (USA), 1995 Other algebras and orders, and their zeta and \(L\)-functions, Varieties over global fields, Global ground fields in algebraic geometry Height preserving linear transformations on semisimple \(K\)-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 Adelic symmetric spaces; Hecke algebras; locally symmetric space Semisimple Lie groups and their representations, Modular and Shimura varieties, Cohomology of arithmetic groups On the cohomology of locally symmetric adele spaces as a module over the Hecke 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 noncommutative polynomials; Kaplansky conjecture; quaternion algebra Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Noncommutative algebraic geometry, Ordinary and skew polynomial rings and semigroup rings The images of noncommutative polynomials evaluated on the quaternion 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 symmetric functions; partitions; Schur functions; Gröbner bases; Grassmannian; cohomology Symmetric functions and generalizations, Grassmannians, Schubert varieties, flag manifolds, Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases), Classical problems, Schubert calculus A quotient of the ring of symmetric functions generalizing quantum cohomology
| 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 hypersurface; torus action; graded algebra; derivation Derivations and commutative rings, Group actions on affine varieties, Actions of groups on commutative rings; invariant theory, Automorphisms of surfaces and higher-dimensional varieties On homogeneous locally nilpotent derivations of trinomial 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 étale algebras; algebra generators; classifying spaces Commutative rings and modules of finite generation or presentation; number of generators, Étale and other Grothendieck topologies and (co)homologies, Classical real and complex (co)homology in algebraic geometry, Motivic cohomology; motivic homotopy theory, Homology of classifying spaces and characteristic classes in algebraic topology Classifying spaces for étale algebras with generators
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces quivers; semi-invariants; tilted algebras Witold Kraśkiewicz, On semi-invariants of tilted algebras of type \?_{\?}, Colloq. Math. 90 (2001), no. 2, 253 -- 267. Representations of quivers and partially ordered sets, Group actions on varieties or schemes (quotients), Trace rings and invariant theory (associative rings and algebras) On semi-invariants of tilted algebras of type \(A_n\)
| 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 Weyl algebra; reflexive modules; torsion free modules; norm; curvature; connection; Jacobian problem; Dixmier conjecture; non-commutative algebraic geometry Jacobian problem, Noncommutative algebraic geometry Reflexive modules of rank one over Weyl algebras of non-zero characteristics
| 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 \(p\)-adic group; representation spaces; Bruhat-Tits building Local ground fields in algebraic geometry, de Rham cohomology and algebraic geometry, Linear algebraic groups over local fields and their integers, Groups with a \(BN\)-pair; buildings, Modular and Shimura varieties Cohomology of Drinfeld symmetric spaces and harmonic cochains
| 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 partial flag varieties; cluster algebras; based affine space; exceptional group; algebraic group; unipotent radical Gautam, S., Cluster algebras and Grassmannians of type \(G_2\), Algebras Represent. Theory, 13, 335-357, (2010) Cluster algebras, Combinatorial aspects of representation theory, Grassmannians, Schubert varieties, flag manifolds Cluster algebras and Grassmannians 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 tensors; symmetric tensors; rank of tensor; symmetric rank of symmetric tensor; border ranks; best \(k\)-approximation of tensors S. Friedland, \textit{Remarks on the symmetric rank of symmetric tensors}, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 320--337, . Multilinear algebra, tensor calculus, Grassmannians, Schubert varieties, flag manifolds, Semialgebraic sets and related spaces, Uniqueness of best approximation, Abstract approximation theory (approximation in normed linear spaces and other abstract spaces), Spaces of operators; tensor products; approximation properties Remarks on the symmetric rank of symmetric tensors
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces equivariant Ray-Singer torsion; symmetric spaces Köhler, K.: Equivariant Reidemeister torsion on symmetric spaces. Math. ann. 307, 57-69 (1997) Determinants and determinant bundles, analytic torsion, Differential geometry of symmetric spaces, Arithmetic varieties and schemes; Arakelov theory; heights Equivariant Reidemeister torsion 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 level of algebra; orbit closure; degeneration; nilpotent algebra General theory of nonassociative rings and algebras, Families, moduli, classification: algebraic theory, Group actions on varieties or schemes (quotients) Anticommutative Engel algebras of the first five levels
| 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 Geiss, C.; Leclerc, B.; Schröer, J., Semicanonical bases and preprojective algebras II: a multiplication formula, Compos. Math., 143, 1313-1334, (2007) Universal enveloping (super)algebras, Special varieties, Representations of quivers and partially ordered sets, Quantum groups (quantized enveloping algebras) and related deformations, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Representation theory for linear algebraic groups Semicanonical bases and preprojective algebras. II: A multiplication formula
| 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 SUSY algebraic curves; quantum supergroups; quantum general linear group; Hopf superalgebra; Flag superspaces; Schubert supercells Manin, Y. I. 1991. ''Topics in Noncommutative Geometry''. Princeton Univ. Press. Noncommutative geometry (à la Connes), Quantum groups (quantized enveloping algebras) and related deformations, Research exposition (monographs, survey articles) pertaining to global analysis, Hopf algebras and their applications, Ring-theoretic aspects of quantum groups, Supermanifolds and graded manifolds, Noncommutative differential geometry, ``Super'' (or ``skew'') structure, Noncommutative algebraic geometry, Quantum groups and related algebraic methods applied to problems in quantum theory, Two-dimensional field theories, conformal field theories, etc. in quantum mechanics, Supersymmetry and quantum mechanics, Noncommutative topology Topics 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 Poonen, B., The moduli space of commutative algebras of finite rank, \textit{J. Eur. Math. Soc. (JEMS)}, 10, 3, 817-836, (2008) Algebraic moduli problems, moduli of vector bundles, Commutative Artinian rings and modules, finite-dimensional algebras, Finite commutative rings, Parametrization (Chow and Hilbert schemes) The moduli space of commutative algebras of finite rank
| 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 Eynard, B., Orantin, N.: About the \(x\)-\(y\) symmetry of the \(F_g\) algebraic invariants. arXiv:1311.4993 (2013) String and superstring theories; other extended objects (e.g., branes) in quantum field theory, String and superstring theories in gravitational theory, Groups and algebras in quantum theory and relations with integrable systems, (Co)homology theory in algebraic geometry, Relationships between algebraic curves and integrable systems, Relationships between algebraic curves and physics Topological expansion of mixed correlations in the Hermitian 2-matrix model and \(x-y\) symmetry of the \(F_{g}\) algebraic invariants
| 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 Fathizadeh, F., On the scalar curvature for the noncommutative four torus, J. Math. Phys., 56, 062303, (2015) Noncommutative geometry (à la Connes), Methods of global Riemannian geometry, including PDE methods; curvature restrictions, Toric varieties, Newton polyhedra, Okounkov bodies, Noncommutative differential geometry On the scalar curvature for the noncommutative four torus
| 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 curves; orbit algebra; concentrated tubes; noncommutative multiplicity; graded factorial domain D. Kussin, \textit{Memoirs of the American Mathematical Society. Vol. 201: Noncommutative curves of genus zero: related to finite dimensional algebras}, AMS Press, Providence U.S.A. (2009). Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Representations of associative Artinian rings, Special algebraic curves and curves of low genus Noncommutative curves of genus zero. Related to finite dimensional 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 partially symmetric rank; cactus rank; tensor rank; W-state; entanglement Secant varieties, tensor rank, varieties of sums of powers, Multilinear algebra, tensor calculus, Rational and unirational varieties On the partially symmetric rank of tensor products of \(W\)-states and other symmetric tensors
| 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 operations Quantum measurement theory, state operations, state preparations, Operator spaces and completely bounded maps, Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), Applications of group representations to physics and other areas of science, Formal methods and deformations in algebraic geometry On the noncommutative deformation of the operator graph corresponding to the Klein group
| 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 Deformed \(W\)-algebras in type \(A\) for rectangular nilpotent
| 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 Burnside theorem; non-commutative deformation theory; Massey product Noncommutative algebraic geometry, Local deformation theory, Artin approximation, etc. A standard example in noncommutative deformation theory
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces discrete integrable systems; non-commutative Hirota-Miwa equation; Yang-Baxter maps; symmetric group; Mal'cev-Neumann series; context-free languages Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), Lattice dynamics; integrable lattice equations, Yang-Baxter equations, Partial difference equations, Integrable difference and lattice equations; integrability tests, Birational automorphisms, Cremona group and generalizations, Skew fields, division rings The Coxeter relations and KP map for non-commuting symbols
| 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 semi-algebraic sets; isotypic decomposition; Specht module; Betti numbers; mirrored spaces; computational complexity Semialgebraic sets and related spaces, Topology of real algebraic varieties, Symmetric functions and generalizations, Effectivity, complexity and computational aspects of algebraic geometry, Symbolic computation and algebraic computation Vandermonde varieties, mirrored spaces, and the cohomology of symmetric semi-algebraic 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 coisotropic algebra; projective coisotropic module; Serre-Swan theorem; foliation; vector bundles Projective and free modules and ideals in commutative rings, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Free, projective, and flat modules and ideals in associative algebras, Linear and affine connections, Foliations (differential geometric aspects), Poisson manifolds; Poisson groupoids and algebroids A Serre-Swan theorem for coisotropic 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 compact symmetric spaces; magic square; division algebras Huang Y.: A uniform description of Riemannian symmetric spaces as Grassmannians using magic square. http://www.ims.cuhk.edu.hk/~leung/ Differential geometry of symmetric spaces, Grassmannians, Schubert varieties, flag manifolds, Nonassociative division algebras A uniform description of compact symmetric spaces as Grassmannians using the magic square
| 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 hypersurface singularity; weighted homogeneous ideal; moduli algebra Singularities of surfaces or higher-dimensional varieties, Local rings and semilocal rings, Local complex singularities, Deformations of singularities A necessary and sufficient condition for a local commutative algebra to be a moduli algebra: Weighted homogeneous case
| 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 products and Jacobians , Amer. J. Math. 83 (1961), 189-206. JSTOR: Jacobians, Prym varieties, Vector bundles on curves and their moduli, Homology of classifying spaces and characteristic classes in algebraic topology, (Equivariant) Chow groups and rings; motives Symmetric products and Jacobians
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; projective geometry; Koszul duality; algebraic \(K\)-theory; cyclic homology and its variants; topological Hochschild homology Noncommutative algebraic geometry, Projective techniques in algebraic geometry, Quadratic and Koszul algebras, \(K\)-theory and homology; cyclic homology and cohomology, \(K\)-theory of schemes Invariants of noncommutative projective schemes
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Infinite-dimensional Lie (super)algebras, Graded Lie (super)algebras, Surfaces and higher-dimensional varieties Almost graded current algebras on the symmetric square of a curve
| 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 pointed Hopf algebras; Frobenius-Lusztig kernels; algebras of distributions Angiono, Iván Ezequiel, A quantum version of the algebra of distributions of {\({\mathrm SL}_2\)}, Publications of the Research Institute for Mathematical Sciences, 54, 1, 141-161, (2018) Affine algebraic groups, hyperalgebra constructions, Quantum groups (quantized enveloping algebras) and related deformations, Hopf algebras and their applications, Linear algebraic groups over arbitrary fields A quantum version of the algebra of distributions of \(\mathrm{SL}_2\)
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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 Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture), Calabi-Yau manifolds (algebro-geometric aspects), Elliptic curves Algebraic aspects of noncommutative tori. The Riemann--Hilbert correspondence
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Ind-pro-schemes; chiral de Rham complex Kapranov, M; Vasserot, E, Vertex algebras and the formal loop space, Publ. Math. Inst. Hautes Études Sci., 100, 206-269, (2004) Vertex operators; vertex operator algebras and related structures, de Rham cohomology and algebraic geometry Vertex algebras and the formal loop 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 diagonal binary form; Clifford algebra; matrix rings; crossed-products; coordinate ring; plane curve T. J. Hodges and S. B. Tesser, Representing Clifford algebras as crossed-products, Journal of Algebra 123 (1989) 500--505. Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Clifford algebras, spinors, Brauer groups of schemes, Endomorphism rings; matrix rings, Special algebraic curves and curves of low genus, Forms of degree higher than two Representing Clifford algebras as crossed-products
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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; coarse moduli schemes; Morita equivalence classes; Deligne-Mumford curves D. Chan and C. Ingalls, Non-commutative coordinate rings and stacks, \textit{Proc. London Math. Soc.,}\textbf{88} (2004), 63-88. Noncommutative algebraic geometry, Generalizations (algebraic spaces, stacks), Rings arising from noncommutative algebraic geometry Non-commutative coordinate rings and stacks
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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 Schur functions; \(\lambda\)-rings; Cauchy kernel; Euclidean algorithm; continued fractions; Padé approximation; divided differences; cohomology of Grassmannian; orthogonal polynomials; Schubert polynomials Lascoux, A.: Symmetric functions \& combinatorial operators on polynomials. CBMS reg. Conf. ser. Math. 99 (2003) Symmetric functions and generalizations, Combinatorial aspects of representation theory, Grassmannians, Schubert varieties, flag manifolds, Representations of finite symmetric groups, Approximation by polynomials, Padé approximation, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis Symmetric functions and combinatorial operators on 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 Yu. A. Drozd and D. E. Voloshyn, ''Vector bundles over noncommutative nodal curves,'' Ukr. Mat. Zh., 64, No. 2, 185--199 (2012); English translation: Ukr. Math. J., 64, No. 2, 208--224 (2012). Noncommutative algebraic geometry, Vector bundles on curves and their moduli Vector bundles over noncommutative nodal 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 Brauer-Picard group; finite tensor category; symmetric monoidal category; cohomology groups Braided monoidal categories and ribbon categories, Symmetric monoidal categories, Brauer groups of schemes Coring categories and Villamayor-Zelinsky sequence for symmetric finite tensor categories
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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 Brauer group; Azumaya algebras; Amitsur cohomology; Teichmüller cocycle map; cohomology group; Picard groups; tensor powers; Chase-Rosenberg long exact sequence; Galois extension; Hopf algebra; dual Hopf algebra; comodule algebra Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Brauer groups of schemes, (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.), Galois theory and commutative ring extensions, Twisted and skew group rings, crossed products Generalized crossed products and Azumaya 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 transserial asymptotic expansions; quasianalyticity; Hardy fields; analysable functions Real-analytic and semi-analytic sets, Model theory of fields, Model theory of ordered structures; o-minimality, Differential algebra, Model-theoretic algebra, Rate of growth of functions, orders of infinity, slowly varying functions, Asymptotic approximations, asymptotic expansions (steepest descent, etc.), Asymptotic representations in the complex plane, Flows on surfaces Ilyashenko algebras based on transserial asymptotic expansions
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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 topological algebras; geometric topological algebras; Gel'fand presheaf; topological algebra scheme; locally affine; local information; Yoneda functor; Yoneda's lemma; functor of points, spectrum functor; Šilov's problem; dynamical algebra; dynamical relativistic localization; Einstein topological algebra space; extension of scalars functor; abstract/modern differential geometry; ADG; Heisenberg's incompatibility; principle of locality Mallios, A.: On algebra spaces. Contemp. Math. 427, 263--283 (2007) Representations of commutative topological algebras, Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.), Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Generalizations (algebraic spaces, stacks), Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory, Axiomatic quantum field theory; operator algebras, Einstein's equations (general structure, canonical formalism, Cauchy problems), Quantization of the gravitational field On algebra 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 bibliography; Hilbert's basis theorem; dictionary: commutative algebra-projective algebraic geometry; Hilbert's syzygy theorem; Hilbert's Nullstellensatz; Hilbert polynomials; dimension theory; Dedekind domains; Hilbert-Samuel functions; elimination theory; computer algebra; modules of differentials; homological methods; Koszul complex; Cohen-Macaulay property; duality theory; linkage Eisenbud D, \textit{Commutative Algebra: With a View Toward Algebraic Geometry}, 150, Springer New York, 1995. Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry, History of commutative algebra, General commutative ring theory, Theory of modules and ideals in commutative rings, Actions of groups on commutative rings; invariant theory, Dimension theory, depth, related commutative rings (catenary, etc.) Commutative algebra. With a view toward 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 Azumaya algebra; involution; Brauer group; sheaf cohomology; equivariant homotopy theory; ramification Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Brauer groups of schemes, Bilinear and Hermitian forms, Equivariant homotopy theory in algebraic topology Involutions of Azumaya 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 representation of the symmetric group; Pieri rule; Gromov-Witten invariants; Schubert polynomials; cohomology ring of the flag manifold; divided difference operators; quadratic associative algebra; Dunkl operators; Schubert calculus; quantum cohomology Fomin, Sergey; Kirillov, Anatol N., Quadratic algebras, Dunkl elements, and Schubert calculus. Advances in geometry, Progr. Math. 172, 147-182, (1999), Birkhäuser Boston, Boston, MA Grassmannians, Schubert varieties, flag manifolds Quadratic algebras, Dunkl elements, and Schubert calculus
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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 category theory; homological algebra; \(K\)-theory; non-commutative localization; triangulated categorie; weight structure; birational motive; \(t\)-structure; algebraic geometry Localization of categories, calculus of fractions, Associative rings of fractions and localizations, (Equivariant) Chow groups and rings; motives, Preadditive, additive categories, Motivic cohomology; motivic homotopy theory, Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects), Ore rings, multiplicative sets, Ore localization, Chain complexes (category-theoretic aspects), dg categories, Grothendieck groups, \(K\)-theory, etc. Non-commutative localizations of additive categories and weight structures
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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 \(W\)-algebras; conformal field theory; isomonodromic deformations 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, Isomonodromic deformations for ordinary differential equations in the complex domain, Structure of families (Picard-Lefschetz, monodromy, etc.), Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups Higher-rank isomonodromic deformations and \(W\)-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 Mirror symmetry (algebro-geometric aspects), Cluster algebras Mirror symmetry and cluster 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 algebra; mutations; helices; stable module category of a selfinjective algebra; exceptional sequence of coherent sheaves; derived category; tilting sheaf DOI: 10.1007/BF02572609 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials, Ext and Tor, generalizations, Künneth formula (category-theoretic aspects), Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects), Representations of quivers and partially ordered sets, Module categories in associative algebras Consistent algebras and special tilting sequences
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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 Symposium; Proceedings; Kyoto (Japan); RIMS; Representation theory; Noncommutative harmonic analysis Proceedings of conferences of miscellaneous specific interest, Proceedings, conferences, collections, etc. pertaining to abstract harmonic analysis, Proceedings, conferences, collections, etc. pertaining to algebraic geometry, Proceedings, conferences, collections, etc. pertaining to nonassociative rings and algebras Representation theory and noncommutative harmonic analysis. Proceedings of a symposium held at the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan, August 3--6, 1998
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Vertex operators; vertex operator algebras and related structures, Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations, Arcs and motivic integration Singular support of a vertex algebra and the arc space of its associated scheme
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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 Projective techniques in algebraic geometry, Multilinear algebra, tensor calculus Linear subspaces of symmetric tensors whose non-zero elements have at least a prescribed rank
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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 Wightman functions; CPT theorem M. Chaichian, M. N. Mnatsakanova, K. Nishijima, A. Tureanu, and Yu. A. Vernov, ''Towards an axiomatic formulation of noncommutative field theories,'' arXiv:hep-th/0402212v1 (2004). Noncommutative geometry methods in quantum field theory, Axiomatic quantum field theory; operator algebras, Deformation quantization, star products, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory), Finite-dimensional groups and algebras motivated by physics and their representations Toward an axiomatic formulation of noncommutative quantum field theory
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces non-commutative geometry; space-time symmetries Noncommutative geometry methods in quantum field theory, Finite-dimensional groups and algebras motivated by physics and their representations, Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) Covariant quantum fields on noncommutative spacetimes
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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 DOI: 10.1088/1751-8113/42/1/015206 String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Noncommutative geometry in quantum theory, Calabi-Yau manifolds (algebro-geometric aspects) Mirror duality and noncommutative tori
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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 local-global domain; central separable \(R\)-algebra; indecomposable finitely generated projective \(A\)-modules; projective class group Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.), Projective and free modules and ideals in commutative rings, Structure, classification theorems for modules and ideals in commutative rings, Brauer groups of schemes Central separable algebras over local-global rings. I
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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 reductive group; spherical variety; parabolic subgroup He, X.; Nishiyama, K.; Ochiai, H.; Oshima, Y., On orbits in double flag varieties for symmetric pairs, Transform. Groups, 18, 4, 1091-1136, (2013) Group actions on varieties or schemes (quotients), Homogeneous spaces and generalizations, Compactifications; symmetric and spherical varieties On orbits in double flag varieties for symmetric pairs
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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 3-dimensional commutative algebras; plane quartics P. Katsylo, D. Mikhailov, Ternary quartics and 3-dimensional commutative algebras. J.~Lie Theory, 7 (2), 165--169 (1997) Plane and space curves, Other algebras built from modules, Theory of modules and ideals in commutative rings Ternary quartics and 3-dimensional commutative 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 Ringel-Hall algebra; constructible set; variety; universal enveloping algebra Ding M, Xiao J, Xu F. Realizing enveloping algebras via varieties of modules. Acta Math Sinica Engl Ser, 2010, 26:29--48 Universal enveloping (super)algebras, Special varieties, Representations of quivers and partially ordered sets Realizing enveloping algebras via varieties of modules
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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 crepant resolution; Rees ring; homologically homogeneous rings; tame orders J. T. Stafford and M. Van den Bergh, Noncommutative resolutions and rational singularities, Michigan Math. J. 57 (2008), 659-674. Special volume in honor of Melvin Hochster. Noncommutative algebraic geometry, Global theory and resolution of singularities (algebro-geometric aspects), Rings arising from noncommutative algebraic geometry, Homological dimension (category-theoretic aspects) Noncommutative resolutions and rational 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 quantum groups; noncommutative spaces; Poincaré; Minkowski spacetime; worldlines; light-like geodesics; Poisson homogeneous spaces; \(\kappa\)-deformation Quantum groups and related algebraic methods applied to problems in quantum theory, Quantum groups (quantized enveloping algebras) and related deformations, Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.), Structure and representation of the Lorentz group, Minkowski geometries in nonlinear incidence geometry, Variational problems in applications to the theory of geodesics (problems in one independent variable), Homogeneous spaces and generalizations, Formal methods and deformations in algebraic geometry The noncommutative space of light-like worldlines
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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 bijective cocycle; brace; hereditary order; non-commutative curve; prime factorization; divisor group; right \(\ell\)-group; quasi-Garside group Yang-Baxter equations, Noncommutative algebraic geometry, Ordered semigroups and monoids, Representation of semigroups; actions of semigroups on sets, Relations with noncommutative geometry, Semihereditary and hereditary rings, free ideal rings, Sylvester rings, etc., Braid groups; Artin groups, Group actions on combinatorial structures Bijective 1-cocycles, braces, and non-commutative prime factorization
| 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 local Nullstellensatz; Banach algebras; firm spectrum; constructive mathematics Constructive and recursive analysis, General theory of topological algebras, Constructive functional analysis, Relevant commutative algebra Finitely generated Banach algebras and local Nullstellensätze
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces finite groups; linear representations; algebras of invariants; codimension; defect Ordinary representations and characters, Vector and tensor algebra, theory of invariants, Group actions on varieties or schemes (quotients), Representation theory for linear algebraic groups, Representations of finite symmetric groups On algebras of invariants of finite groups
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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 irreducible Hermitian symmetric space; principal bundle; pure connexions; normal variety Homogeneous complex manifolds, Homogeneous spaces and generalizations, Holomorphic bundles and generalizations A normal variety of invariant connexions on Hermitian 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 central simple algebras; involutions of orthogonal type; generic algebras; Clifford algebras; signed discriminants; quaternion algebras; Brauer equivalence Tao D.: The generalized even Clifford algebra. J. Algebra 172, 184--204 (1995) Rings with involution; Lie, Jordan and other nonassociative structures, Finite-dimensional division rings, Clifford algebras, spinors, Brauer groups of schemes, Homogeneous spaces and generalizations, Computations of higher \(K\)-theory of rings, Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) The generalized even Clifford 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 abelian subvariety of Jacobian; symmetric correspondences; vanishing theorems; projective smooth curve; symmetric product Alzati, A; Pirola, GP, On abelian subvarieties generated by symmetric correspondences, Math. Z., 205, 333-342, (1990) Jacobians, Prym varieties, Algebraic theory of abelian varieties, Vanishing theorems in algebraic geometry, Vanishing theorems On abelian subvarieties generated by symmetric correspondences
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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 Actions of groups on commutative rings; invariant theory, Group actions on varieties or schemes (quotients), Vector and tensor algebra, theory of invariants, Trace rings and invariant theory (associative rings and algebras) Characteristic free description of semi-invariants of \(2 \times 2\) 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 quasihomogeneous polynomials; invertible polynomials; singularities Local complex singularities, Singularities in algebraic geometry, Polynomials and rational functions of several complex variables On Milnor algebras of invertible 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 reductive group; freeness of invariant polynomials; slice Other algebraic groups (geometric aspects), Actions of groups on commutative rings; invariant theory, Representation theory for linear algebraic groups, Geometric invariant theory On non-connected simple linear groups with a free algebra of invariants
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces noncommutative algebraic geometry; curves; noncommutative model; factorization Jøndrup, S.: Factorization in noncommutative curves, Linear algebra appl. 431, 985-990 (2009) Noncommutative algebraic geometry, Plane and space curves, Affine geometry, Simple and semisimple modules, primitive rings and ideals in associative algebras, Representations of orders, lattices, algebras over commutative rings Factorization in noncommutative 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 nonnoetherian ring; nonnoetherian geometry; dimer algebra; Calabi-Yau singularity Noncommutative algebraic geometry, String and superstring theories; other extended objects (e.g., branes) in quantum field theory, Rings arising from noncommutative algebraic geometry, Dimension theory, depth, related commutative rings (catenary, etc.) On the central geometry of nonnoetherian dimer 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 minuscule representations; exceptional simple Lie algebras; del Pezzo surfaces; invariant tensors [75] Lurie J., ''On simply laced Lie algebras and their minuscule representations'', Comment. Math. Helv., 166 (2001), 515--575 Exceptional (super)algebras, Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Rational and ruled surfaces On simply laced Lie algebras and their minuscule representations
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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Khovanov-Lauda-Rouquier algebra; Borcherds-Cartan matrix; quiver varieties; global basis; categorification Kang, S. -J.; Kashiwara, M.; Park, E.: Geometric realization of Khovanov-lauda-Rouquier algebras associated with borcherds-Cartan data. Proc. lond. Math. soc. (3) 107, 907-931 (2013) Quantum groups (quantized enveloping algebras) and related deformations, Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras, Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations Geometric realization of Khovanov-Lauda-Rouquier algebras associated with Borcherds-Cartan data
| 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 covering of curves; gonality; syzygy; Galois coverings of curves; scrollar invariants. Scrollar invariants, syzygies and representations of the symmetric group
| 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 Kleinian singularities; deformed preprojective algebras; McKay graphs; deformations Crawley-Boevey, W.; Holland, M. P., \textit{noncommutative deformations of Kleinian singularities}, Duke Math. J., 92, 605-635, (1998) Representations of associative Artinian rings, Deformations of singularities, Deformations of associative rings, Noncommutative algebraic geometry, Rings of differential operators (associative algebraic aspects) Noncommutative deformations of Kleinian 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 infinite-dimensional Lie algebras; current algebras; Krichever-Novikov type algebras; central extensions; Lie algebra cohomology; integrable systems M. Schlichenmaier, ''Multipoint Lax operator algebras: Almost graded structure and central extensions,'' ArXiv:1304.3902. Infinite-dimensional Lie (super)algebras, Virasoro and related algebras, Cohomology of Lie (super)algebras, Relationships between algebraic curves and integrable systems Multipoint Lax operator algebras: almost-graded structure and central extensions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces Noncommutative geometry in quantum theory, Appell, Horn and Lauricella functions, Formal methods and deformations in algebraic geometry, Cyclotomic function fields (class groups, Bernoulli objects, etc.), Structure and representation of the Lorentz group Generalized Heisenberg algebra applied to realizations of the orthogonal, Lorentz, and Poincaré algebras and their dual extensions
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces index of Lie algebra; coadjoint representation; symmetric invariants D. Panyushev, O. Yakimova: \textit{Symmetric invariants related to representations of} \textit{exceptional simple groups}, Trans. Moscow Math. Soc. 78 (2017) 161--170. Group actions on varieties or schemes (quotients), Coadjoint orbits; nilpotent varieties, Simple, semisimple, reductive (super)algebras, Semisimple Lie groups and their representations Symmetric invariants related to representations of exceptional simple groups
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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 derived category; semiorthogonal decomposition; projective duality; noncommutative algebraic geometry Noncommutative algebraic geometry, Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.), Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Rings arising from noncommutative algebraic geometry Noncommutative homological projective duality
| 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 vanishing theorems; invertible sheaves; Noetherian graded rings; invertible bimodules; projective schemes; coordinate rings; tensor products; ampleness; Rees rings; Gelfand-Kirillov dimension Dennis S. Keeler, Noncommutative ampleness for multiple divisors, J. Algebra 265 (2003), no. 1, 299 -- 311. Rings arising from noncommutative algebraic geometry, Noncommutative algebraic geometry, Divisors, linear systems, invertible sheaves, Schemes and morphisms, Vanishing theorems in algebraic geometry, Growth rate, Gelfand-Kirillov dimension, Graded rings and modules (associative rings and algebras), Automorphisms of surfaces and higher-dimensional varieties Noncommutative ampleness for multiple divisors
| 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-module; trace function; sub-holonomic system Sheaves of differential operators and their modules, \(D\)-modules, Riemann-Hilbert problems in context of PDEs, Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials On symmetric partial differential operators
| 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; twisted homogeneous coordinate rings; abstract Hilbert schemes Keeler, D. S.: The rings of noncommutative projective geometry. Advances in algebra and geometry, 195-207 (2003) Noncommutative algebraic geometry, Projective techniques in algebraic geometry, Noetherian rings and modules (associative rings and algebras) The rings of noncommutative projective 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 tori; real multiplication; theta functions; quadratic algebra Plazas, J.: Arithmetic structures on noncommutative tori with real multiplication. Int. Math. Res. Not. IMRN 2008, no. 2, Art. ID rnm147 Noncommutative algebraic geometry, Noncommutative geometry (à la Connes), Relations with noncommutative geometry, Theta series; Weil representation; theta correspondences, Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols, Elliptic curves over global fields, Noncommutative differential geometry, Noncommutative geometry in quantum theory, Quadratic and Koszul algebras Arithmetic structures on noncommutative tori with real multiplication
| 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 Research exposition (monographs, survey articles) pertaining to algebraic geometry, Noncommutative algebraic geometry, Elliptic curves Arithmetic structures on noncommutative tori with real multiplication
| 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 coordinate ring; base affine space; classical groups; invariant theory DOI: 10.1016/0021-8693(85)90185-1 Classical groups (algebro-geometric aspects), Affine algebraic groups, hyperalgebra constructions, Linear algebraic groups over adèles and other rings and schemes, Vector and tensor algebra, theory of invariants, Homogeneous spaces and generalizations Representation functors and flag-algebras for the classical groups. 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 matrix multiplication complexity; border rank; tensor; commuting matrices; Strassen's equations; determinant; normal forms Landsberg, JM; Michałek, M., On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetry, SIAM J. Appl. Algebra Geom., 1, 2-19, (2017) Multilinear algebra, tensor calculus, Vector spaces, linear dependence, rank, lineability, Determinants, permanents, traces, other special matrix functions, Effectivity, complexity and computational aspects of algebraic geometry, Homogeneous spaces and generalizations On the geometry of border rank decompositions for matrix multiplication and other tensors with 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 cobordism; \(K\)-theory; flag varieties; symmetric varieties Kiritchenko, V; Krishna, A, Equivariant cobordism of flag varieties and of symmetric varieties, Transf. Groups, 18, 391-413, (2013) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies), Grassmannians, Schubert varieties, flag manifolds Equivariant cobordism of flag varieties and of symmetric varieties
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces branching law; restriction of representation; reductive group; real spherical variety; symmetric pair Semisimple Lie groups and their representations, Grassmannians, Schubert varieties, flag manifolds, Differential geometry of symmetric spaces Symmetric pairs with finite-multiplicity property for branching laws of admissible representations
| 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Rings arising from noncommutative algebraic geometry, Endomorphism rings; matrix rings, Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.), Associative rings of functions, subdirect products, sheaves of rings, Noncommutative algebraic geometry, Rational and ruled surfaces Noncommutative symmetric algebras of two-sided vector spaces homological mirror symmetry; elliptic curves; LG/CY correspondence; matrix factorizations Mirror symmetry (algebro-geometric aspects), Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category, Derived categories of sheaves, dg categories, and related constructions in algebraic geometry, Elliptic curves Noncommutative homological mirror symmetry of 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 non-commutative desingularization; sparse spectral sequence; simple representations; tautological Koszul complex; maximal Cohen-Macaulay; quivers; Clifford algebra Abhyankar, S.: Uniformization in a \( p\)-cyclic extension of a two dimensional regular local domain of residue field characteristic \( p\) . Festschrift zur Gedächtnisfeier für Karl Weierstrass 1815 - 1965, Wissenschaftliche Abhandlungen des Landes Nordrhein-Westfalen \textbf{33} (1966), 243-317, Westdeutscher Verlag, Köln und Opladen Noncommutative algebraic geometry, Cohen-Macaulay modules, Global theory and resolution of singularities (algebro-geometric aspects), Riemann-Roch theorems, Rings arising from noncommutative algebraic geometry, Syzygies, resolutions, complexes and commutative rings, Representations of quivers and partially ordered sets Non-commutative desingularization of determinantal varieties. 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 Fukaya category; homological mirror symmetry; noncommutative algebra; Landau-Ginzburg model; deformation quantization Research exposition (monographs, survey articles) pertaining to algebraic geometry, Mirror symmetry (algebro-geometric aspects), Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category Noncommutative homological mirror functor
| 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 homogeneous varieties; toric varieties; twisted forms; torsors; noncommutative motives; algebraic \(K\)-theory; cyclic homology; noncommutative algebraic geometry Tabuada, G, Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives, J. Algebra, 417, 15-38, (2014) \(K\)-theory of schemes, Applications of methods of algebraic \(K\)-theory in algebraic geometry, Noncommutative algebraic geometry, Affine algebraic groups, hyperalgebra constructions, Toric varieties, Newton polyhedra, Okounkov bodies, Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects), \(K\)-theory and homology; cyclic homology and cohomology Additive invariants of toric and twisted projective homogeneous varieties via noncommutative motives
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