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Topological tensor product of bimodules, complete Hopf algebroids and convolution algebras

Communications in Contemporary Mathematics, ISSN 0219-1997, 09/2019, Volume 21, Issue 6, p. 1850015

Given a finitely generated and projective Lie–Rinehart algebra, we show that there is a continuous homomorphism of complete commutative Hopf algebroids...

co-commutative Hopf algebroids | Complete commutative Hopf algebroids | Lie algebroids | completion 2-functor | topological tensor product | adic topology | convolution algebras | filtered bimodules | finite dual | Lie–Rinehart algebras | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Rinehart algebras | Algebra

co-commutative Hopf algebroids | Complete commutative Hopf algebroids | Lie algebroids | completion 2-functor | topological tensor product | adic topology | convolution algebras | filtered bimodules | finite dual | Lie–Rinehart algebras | MATHEMATICS | MATHEMATICS, APPLIED | Lie-Rinehart algebras | Algebra

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 09/2017, Volume 60, Issue 3, pp. 470 - 477

In a previous work, we associated a complete differential graded Lie algebra to any finite simplicial complex in a functorial way...

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Rational homotopy theory | Maurer-Cartan elements | Complete differential graded lie algebra | MATHEMATICS | complete differential graded Lie algebra | RATIONAL HOMOTOPY-THEORY | rational homotopy theory

Journal Article

数学学报：英文版, ISSN 1439-8516, 2013, Volume 29, Issue 7, pp. 1279 - 1310

In this paper, we introduce a new numerical invariant complete level for a DG module over a local chain DG algebra and give a characterization of it in terms of ghost length...

数值 | 连锁 | 模块 | 水 | 长度 | 圆锥体 | ghost length | complete level | 16W50 | 16E30 | 16E65 | 14A22 | Mathematics, general | Mathematics | Local chain DG algebra | DG module | 16E45 | cone length | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTABILITY | CATEGORY | DIFFERENTIAL GRADED ALGEBRAS | HOMOLOGY | Algebra | Studies | Ghosts | Chains | Upper bounds | Modules | Invariants

数值 | 连锁 | 模块 | 水 | 长度 | 圆锥体 | ghost length | complete level | 16W50 | 16E30 | 16E65 | 14A22 | Mathematics, general | Mathematics | Local chain DG algebra | DG module | 16E45 | cone length | MATHEMATICS | MATHEMATICS, APPLIED | REPRESENTABILITY | CATEGORY | DIFFERENTIAL GRADED ALGEBRAS | HOMOLOGY | Algebra | Studies | Ghosts | Chains | Upper bounds | Modules | Invariants

Journal Article

Indian Journal of Pure and Applied Mathematics, ISSN 0019-5588, 9/2019, Volume 50, Issue 3, pp. 801 - 834

Operator algebras come in many flavours. For the purpose of this article, however, the term is only used for one of two kinds of self-adjoint algebras of operators on Hilbert space, viz., C*- algebras...

Ergodic theory | operator-algebraic quantum groups | E 0 semigroups on B ( H ), resp., on general factors | quantum isometry groups | (sub- and super-) product systems | semigroup C -algebras | metric properties | Yang Mills functionals | Mathematics | free probability | types I–III of E 0 semigroups | rapid decay property | Mathematics, general | spectral triples for quantum groups | TQFTs, Hopf (and Kac) algebras | Elliott’s classification program | Applications of Mathematics | Masas | q -deformed Araki-Woods von Neumann algebras | Dirac differential graded algebra | C -algebras | noncommutative geometry (NCG) | local index formula in NCG | subfactors | compact quantum metric spaces | complete positivity | extendability of E 0 semigroups | Numerical Analysis | von Neumann algebras | planar algebras | Skein theories | dimensional invariants | quantum dynamical systems | sub | EQUIVARIANT SPECTRAL TRIPLES | E-0 semigroups on B(H) | types I-III of E-0 semigroups | on general factors | CROSSED-PRODUCTS | TQFTs | ERGODIC EQUIVALENCE RELATIONS | Hopf (and Kac) algebras | extendability of E-0 semigroups | LOCAL INDEX FORMULA | MATHEMATICS | q-deformed Araki-Woods von Neumann algebras | TENSOR PRODUCT SYSTEMS | and super-) product systems | resp | C-algebras | C-ASTERISK-ALGEBRAS | TANNAKA-KREIN DUALITY | semigroup C-algebras | Elliott's classification program | AMALGAMATED PRODUCTS | QUANTUM AUTOMORPHISM-GROUPS

Ergodic theory | operator-algebraic quantum groups | E 0 semigroups on B ( H ), resp., on general factors | quantum isometry groups | (sub- and super-) product systems | semigroup C -algebras | metric properties | Yang Mills functionals | Mathematics | free probability | types I–III of E 0 semigroups | rapid decay property | Mathematics, general | spectral triples for quantum groups | TQFTs, Hopf (and Kac) algebras | Elliott’s classification program | Applications of Mathematics | Masas | q -deformed Araki-Woods von Neumann algebras | Dirac differential graded algebra | C -algebras | noncommutative geometry (NCG) | local index formula in NCG | subfactors | compact quantum metric spaces | complete positivity | extendability of E 0 semigroups | Numerical Analysis | von Neumann algebras | planar algebras | Skein theories | dimensional invariants | quantum dynamical systems | sub | EQUIVARIANT SPECTRAL TRIPLES | E-0 semigroups on B(H) | types I-III of E-0 semigroups | on general factors | CROSSED-PRODUCTS | TQFTs | ERGODIC EQUIVALENCE RELATIONS | Hopf (and Kac) algebras | extendability of E-0 semigroups | LOCAL INDEX FORMULA | MATHEMATICS | q-deformed Araki-Woods von Neumann algebras | TENSOR PRODUCT SYSTEMS | and super-) product systems | resp | C-algebras | C-ASTERISK-ALGEBRAS | TANNAKA-KREIN DUALITY | semigroup C-algebras | Elliott's classification program | AMALGAMATED PRODUCTS | QUANTUM AUTOMORPHISM-GROUPS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 12

In this paper, we introduce the concept of normed Lie superalgebras and define the superhomomorphism and the superderivation in normed Lie superalgebras...

Mathematical and Computational Biology | superderivation | Mathematics | Topology | Lie superalgebra | superhomomorphism | 47H10 | Analysis | Mathematics, general | 16W25 | Applications of Mathematics | T -orbitally complete metric space | Differential Geometry | 39B82 | T-orbitally complete metric space | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTIONAL-EQUATIONS | ALGEBRAS | BANACH-SPACES | MAPPINGS | SUPERDERIVATIONS | Usage | Lie superalgebras | Functional equations | Functions | Metric spaces | Research | Fixed points (mathematics) | Stability | Approximation | Metric space | Mathematical analysis

Mathematical and Computational Biology | superderivation | Mathematics | Topology | Lie superalgebra | superhomomorphism | 47H10 | Analysis | Mathematics, general | 16W25 | Applications of Mathematics | T -orbitally complete metric space | Differential Geometry | 39B82 | T-orbitally complete metric space | MATHEMATICS | MATHEMATICS, APPLIED | FUNCTIONAL-EQUATIONS | ALGEBRAS | BANACH-SPACES | MAPPINGS | SUPERDERIVATIONS | Usage | Lie superalgebras | Functional equations | Functions | Metric spaces | Research | Fixed points (mathematics) | Stability | Approximation | Metric space | Mathematical analysis

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 3/2018, Volume 108, Issue 3, pp. 633 - 678

We survey the theory of Poisson traces (or zeroth Poisson homology) developed by the authors in a series of recent papers. The goal is to understand this...

Calabi–Yau varieties | Milnor fibration | 37J05 | Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson homology | 14F10 | Milnor number | Physics | Poisson varieties | Geometry | Symplectic resolutions | Twistor deformations | 32S20 | D-modules | Poisson traces | Group Theory and Generalizations | Kostka polynomials | Hamiltonian flow | Complete intersections | COMPLEX | HOLONOMIC SYSTEMS | SINGULARITIES | LIE-ALGEBRA | VARIETIES | CHEREDNIK ALGEBRAS | Calabi-Yau varieties | PHYSICS, MATHEMATICAL | REPRESENTATION-THEORY | COHOMOLOGY | QUANTIZATION | HOMOLOGY | Algebra

Calabi–Yau varieties | Milnor fibration | 37J05 | Deformation quantization | 53D55 | Theoretical, Mathematical and Computational Physics | Complex Systems | Poisson homology | 14F10 | Milnor number | Physics | Poisson varieties | Geometry | Symplectic resolutions | Twistor deformations | 32S20 | D-modules | Poisson traces | Group Theory and Generalizations | Kostka polynomials | Hamiltonian flow | Complete intersections | COMPLEX | HOLONOMIC SYSTEMS | SINGULARITIES | LIE-ALGEBRA | VARIETIES | CHEREDNIK ALGEBRAS | Calabi-Yau varieties | PHYSICS, MATHEMATICAL | REPRESENTATION-THEORY | COHOMOLOGY | QUANTIZATION | HOMOLOGY | Algebra

Journal Article

Mathematische Zeitschrift, ISSN 0025-5874, 12/2019, Volume 293, Issue 3, pp. 1121 - 1159

Let G be a reductive linear algebraic group, H a reductive subgroup of G and X an affine G-variety. Let $$X^H$$ X H denote the set of fixed points of H in X,...

Quotient variety | 14L24 | Geometric invariant theory | Mathematics, general | G -Complete reducibility | Mathematics | Double cosets | 20G15 | Étale slice | G-Complete reducibility | TUPLES | COMPLETE REDUCIBILITY | INSTABILITY | Etaleslice | ALGEBRAIC-GROUPS | LIE-ALGEBRAS | MATHEMATICS | REDUCTIVE SUBGROUPS | DOUBLE COSET DENSITY | CLOSED ORBITS | CONJUGACY CLASSES

Quotient variety | 14L24 | Geometric invariant theory | Mathematics, general | G -Complete reducibility | Mathematics | Double cosets | 20G15 | Étale slice | G-Complete reducibility | TUPLES | COMPLETE REDUCIBILITY | INSTABILITY | Etaleslice | ALGEBRAIC-GROUPS | LIE-ALGEBRAS | MATHEMATICS | REDUCTIVE SUBGROUPS | DOUBLE COSET DENSITY | CLOSED ORBITS | CONJUGACY CLASSES

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 4/2014, Volume 48, Issue 2, pp. 107 - 115

It is proved that the limit of integrable Hamiltonians on a semisimple Lie algebra is an integrable Hamiltonian...

Functional Analysis | Analysis | semisimple Lie algebra | Hamiltonian system | Mathematics | Poisson algebra | complete integrability | transcendence degree | Gelfand-Kirillov dimension | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Functional Analysis | Analysis | semisimple Lie algebra | Hamiltonian system | Mathematics | Poisson algebra | complete integrability | transcendence degree | Gelfand-Kirillov dimension | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2014, Volume 42, Issue 8, pp. 3507 - 3540

We investigate relations between the properties of an algebra and its varieties of finite-dimensional module structures, on the example of the Jordan plane R = k ⟨ x, y ⟩ /(xy − yx − y 2...

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | 16G60 | MATHEMATICS | VARIETIES | Primary 16G30 | 16D25 | Algebra | Representations | Planes | Intersections | Modules

Irreducible components | (noncommutative complete intersections) NCCI | Primary 16G30, 16G60, 16D25 | Secondary 16A24 | Representation spaces | (representational complete intersections) RCI | Golod-Shafarevich complex | 16G60 | MATHEMATICS | VARIETIES | Primary 16G30 | 16D25 | Algebra | Representations | Planes | Intersections | Modules

Journal Article

Mathematics of the USSR-Izvestiya, ISSN 0025-5726, 02/1992, Volume 38, Issue 1, pp. 69 - 90

.... Several examples of compatible Poisson brackets on duals of Lie algebras are considered, as well as the associated involutive function families and Hamiltonian systems...

MATHEMATICS | SYSTEMS | COMPLETE-INTEGRABILITY | EULER EQUATIONS

MATHEMATICS | SYSTEMS | COMPLETE-INTEGRABILITY | EULER EQUATIONS

Journal Article

Topology (Oxford), ISSN 0040-9383, 2005, Volume 44, Issue 3, pp. 557 - 584

... (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all CR-equivalences or CR-embeddings respectively...

CR-structure | Complete systems | Nondegeneracy conditions | Equivalence problem | Jet parametrization | COMPLETE SYSTEM | PROPER HOLOMORPHIC MAPPINGS | PSEUDOCONVEX DOMAINS | COMPLEX-SPACES | complete systems | nondegencracy conditions | jet parametrization | MATHEMATICS | equivalence problem | REAL-SUBMANIFOLDS | HYPERSURFACES | FINITE-ORDER | MANIFOLDS | REFLECTION PRINCIPLE | LEVI FORMS

CR-structure | Complete systems | Nondegeneracy conditions | Equivalence problem | Jet parametrization | COMPLETE SYSTEM | PROPER HOLOMORPHIC MAPPINGS | PSEUDOCONVEX DOMAINS | COMPLEX-SPACES | complete systems | nondegencracy conditions | jet parametrization | MATHEMATICS | equivalence problem | REAL-SUBMANIFOLDS | HYPERSURFACES | FINITE-ORDER | MANIFOLDS | REFLECTION PRINCIPLE | LEVI FORMS

Journal Article

Sbornik: Mathematics, ISSN 1064-5616, 08/2003, Volume 194, Issue 7-8, pp. 1079 - 1103

It is proved that for any transitive Lie algebroid L on a compact oriented connected manifold with unimodular isotropy Lie algebras and trivial monodromy the cohomology algebra is a Poincare algebra...

MATHEMATICS | TRANSVERSALLY COMPLETE FOLIATIONS

MATHEMATICS | TRANSVERSALLY COMPLETE FOLIATIONS

Journal Article

Selecta Mathematica, ISSN 1022-1824, 7/2016, Volume 22, Issue 3, pp. 1749 - 1791

.... Specifically, we prove such vanishing if $$R = Q/(f_1, \dots , f_c)$$ R = Q / ( f 1 , ⋯ , f c ) has only isolated singularities, Q is a smooth k-algebra, k is a field of characteristic 0...

Chern character | Mathematics, general | Mathematics | Matrix factorization | Hochschild homology | 13D03 | 14B05 | MATHEMATICS, APPLIED | COMPLETE INTERSECTION | THEOREM | HOCHSTERS THETA INVARIANT | HIGHER CODIMENSION | FORMULA | CATEGORIES | MATHEMATICS | MODULES | TOR | HYPERSURFACES | SINGULARITY | Algebra

Chern character | Mathematics, general | Mathematics | Matrix factorization | Hochschild homology | 13D03 | 14B05 | MATHEMATICS, APPLIED | COMPLETE INTERSECTION | THEOREM | HOCHSTERS THETA INVARIANT | HIGHER CODIMENSION | FORMULA | CATEGORIES | MATHEMATICS | MODULES | TOR | HYPERSURFACES | SINGULARITY | Algebra

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2017, Volume 11, Issue 4, pp. 1351 - 1379

We construct the Gerstenhaber bracket on Hochschild cohomology of a twisted tensor product of algebras, and, as examples, compute Gerstenhaber brackets for some quantum complete intersections arising...

Hochschild cohomology | Twisted tensor products | Quantum complete intersections | Gerstenhaber brackets | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | RING | twisted tensor products | quantum complete intersections | PHYSICS, MATHEMATICAL

Hochschild cohomology | Twisted tensor products | Quantum complete intersections | Gerstenhaber brackets | MATHEMATICS | MATHEMATICS, APPLIED | ALGEBRAS | RING | twisted tensor products | quantum complete intersections | PHYSICS, MATHEMATICAL

Journal Article

Communications in Algebra, ISSN 0092-7872, 02/2016, Volume 44, Issue 2, pp. 710 - 730

Given a finite simple graph, one can associate the edge ideal. In this article, we prove that a graded Betti number of the edge ideal does not vanish if the original graph contains a set of complete bipartite subgraphs with some conditions...

Graded Betti numbers | Lyubeznik resolutions | Projective dimension | Edge ideals | Complete bipartite graphs | Primary: 13D02, 13F55 | Secondary: 05C99 | MATHEMATICS | INDEPENDENCE | REGULARITY | BOUNDS | MONOMIAL IDEALS | MINIMAL FREE RESOLUTIONS

Graded Betti numbers | Lyubeznik resolutions | Projective dimension | Edge ideals | Complete bipartite graphs | Primary: 13D02, 13F55 | Secondary: 05C99 | MATHEMATICS | INDEPENDENCE | REGULARITY | BOUNDS | MONOMIAL IDEALS | MINIMAL FREE RESOLUTIONS

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 08/2018, Volume 50, Issue 4, pp. 583 - 597

... can be embedded in weighted projective space by taking the canonical model Proj R ( X ) of X , where R ( X ) is the canonical graded ring R ( X , K X ) = ⨁ n ⩾ 0 H 0 ( X , n...

14Q15 (secondary) | 14J30 (primary) | 14J28 | WEIGHTED COMPLETE-INTERSECTIONS | CALABI-YAU THREEFOLDS | MATHEMATICS | EXPLICIT BIRATIONAL GEOMETRY | GORENSTEIN INDEX 2 | Q-FANO 3-FOLDS | GENERAL TYPE | CLASSIFICATION | Mathematics - Algebraic Geometry

14Q15 (secondary) | 14J30 (primary) | 14J28 | WEIGHTED COMPLETE-INTERSECTIONS | CALABI-YAU THREEFOLDS | MATHEMATICS | EXPLICIT BIRATIONAL GEOMETRY | GORENSTEIN INDEX 2 | Q-FANO 3-FOLDS | GENERAL TYPE | CLASSIFICATION | Mathematics - Algebraic Geometry

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2015, Volume 367, Issue 5, pp. 3323 - 3370

We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations...

MATHEMATICS | COHOMOLOGY | MODULES | DIMENSION | THEOREM | SINGULARITY CATEGORIES | SUPPORT VARIETIES | HOMOLOGICAL ALGEBRA | TRIANGULATED CATEGORIES | COMPLETE-INTERSECTIONS

MATHEMATICS | COHOMOLOGY | MODULES | DIMENSION | THEOREM | SINGULARITY CATEGORIES | SUPPORT VARIETIES | HOMOLOGICAL ALGEBRA | TRIANGULATED CATEGORIES | COMPLETE-INTERSECTIONS

Journal Article

Functional Analysis and Its Applications, ISSN 0016-2663, 10/2018, Volume 52, Issue 4, pp. 241 - 257

In this paper we discuss some problems of the deformation theory of zero-dimensional singularities, which are closely related to the study of properties of differential forms and the Poincaré–de Rham complex...

Poincaré lemma | Functional Analysis | multiple points | vector fields | complete intersections | Analysis | fat points | thick points | Mathematics | differential forms | cotangent homology | determinantal singularities | Poincare lemma | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANTS

Poincaré lemma | Functional Analysis | multiple points | vector fields | complete intersections | Analysis | fat points | thick points | Mathematics | differential forms | cotangent homology | determinantal singularities | Poincare lemma | MATHEMATICS | MATHEMATICS, APPLIED | INVARIANTS

Journal Article

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 1/2017, Volume 38, Issue 1, pp. 1 - 15

Let Q be a smoothmanifold of dimension n ≥ 1. In this paper,we define the vertical lift of multivector fields from Q to T Q and we give some applications in...

Geometry | Algebra | Analysis | vertical and complete lifts of vector fields and 1-forms | Mathematics, general | Probability Theory and Stochastic Processes | natural transformations | Mathematics | Mathematical Logic and Foundations | Nijenhuis manifold

Geometry | Algebra | Analysis | vertical and complete lifts of vector fields and 1-forms | Mathematics, general | Probability Theory and Stochastic Processes | natural transformations | Mathematics | Mathematical Logic and Foundations | Nijenhuis manifold

Journal Article

Geometric and Functional Analysis, ISSN 1016-443X, 12/2014, Volume 24, Issue 6, pp. 1885 - 1912

We consider the Hamiltonian flow on complex complete intersection surfaces with isolated singularities, equipped with the Jacobian Poisson structure. More...

Calabi–Yau varieties | Milnor fibration | 37J05 | Poisson homology | 14F10 | Mathematics | Milnor number | Poisson varieties | 32S20 | D-modules | Analysis | Hamiltonian flow | Complete intersections | MATHEMATICS | SINGULARITIES | HOMOLOGY

Calabi–Yau varieties | Milnor fibration | 37J05 | Poisson homology | 14F10 | Mathematics | Milnor number | Poisson varieties | 32S20 | D-modules | Analysis | Hamiltonian flow | Complete intersections | MATHEMATICS | SINGULARITIES | HOMOLOGY

Journal Article

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