Mathematische Annalen, ISSN 0025-5831, 02/2017, Volume 367, Issue 1-2, pp. 397 - 440

Journal Article

Mathematische Annalen, ISSN 0025-5831, 2/2017, Volume 367, Issue 1, pp. 397 - 440

The trace or the 0th Hochschild–Mitchell homology of a linear category $$\mathcal {C}$$ C may be regarded as a kind of decategorification of $$\mathcal {C}$$ C...

16E40 | 81R50 | Mathematics, general | Mathematics | 17B37

16E40 | 81R50 | Mathematics, general | Mathematics | 17B37

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 7/2019, Volume 113, Issue 1, pp. 1 - 10

In 1941, Brauer-Nesbitt established a characterization of a block with trivial defect group as a block B with $$k(B) = 1$$ k ( B ) = 1 where k(B) is the number...

16E40 | Morita equivalence | Codimension | 20C20 | Secondary 16P10 | Commutator subspace | Mathematics, general | Mathematics | Finite-dimensional algebra | Morita invariant | Primary 16G10 | MATHEMATICS | Algebra

16E40 | Morita equivalence | Codimension | 20C20 | Secondary 16P10 | Commutator subspace | Mathematics, general | Mathematics | Finite-dimensional algebra | Morita invariant | Primary 16G10 | MATHEMATICS | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2019, Volume 47, Issue 8, pp. 3384 - 3398

We show that faithfully flat smooth extensions of associative unital algebras are reduced flat, and therefore, fit into the Jacobi-Zariski exact sequence in...

Jacobi-Zariski | algebra extensions | Hochschild homology | noncommutative algebras | 16E40; 14A22 | MATHEMATICS | CYCLIC HOMOLOGY | Homology | Combinatorial analysis

Jacobi-Zariski | algebra extensions | Hochschild homology | noncommutative algebras | 16E40; 14A22 | MATHEMATICS | CYCLIC HOMOLOGY | Homology | Combinatorial analysis

Journal Article

Selecta Mathematica, ISSN 1022-1824, 7/2016, Volume 22, Issue 3, pp. 1583 - 1612

We define a functorial spectrum-level filtration on the topological Hochschild homology of any commutative ring spectrum R, and more generally the...

16E40 | Mathematics, general | Mathematics | 55P42 | 18F25 | MATHEMATICS | MATHEMATICS, APPLIED

16E40 | Mathematics, general | Mathematics | 55P42 | 18F25 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Selecta Mathematica, ISSN 1022-1824, 7/2016, Volume 22, Issue 3, pp. 1537 - 1561

Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify...

16E40 | Mathematics, general | Mathematics | 16S35 | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

16E40 | Mathematics, general | Mathematics | 16S35 | MATHEMATICS | MATHEMATICS, APPLIED | Algebra

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 3/2019, Volume 112, Issue 3, pp. 249 - 259

In this paper, for finite dimensional, basic, and connected algebras over a field, we give a sufficient condition, related to 2-cocycles, for Hochschild...

Primary 16E40 | Mathematics, general | Hochschild cohomology | Mathematics | Symmetric algebras | Hochschild extensions | Secondary 16G10 | 2-Cocycles | MATHEMATICS | Algebra

Primary 16E40 | Mathematics, general | Hochschild cohomology | Mathematics | Symmetric algebras | Hochschild extensions | Secondary 16G10 | 2-Cocycles | MATHEMATICS | Algebra

Journal Article

Bulletin of the London Mathematical Society, ISSN 0024-6093, 02/2017, Volume 49, Issue 1, pp. 95 - 101

Using the E∞‐structure on singular co‐chains, we construct a homotopy coherent map from the cyclic bar construction of the differential graded algebra of...

16E40 | 55S20 (secondary) | 19D55 | 55P35 (primary) | 55P50 | MATHEMATICS | HOMOLOGY | Mathematics - Algebraic Topology

16E40 | 55S20 (secondary) | 19D55 | 55P35 (primary) | 55P50 | MATHEMATICS | HOMOLOGY | Mathematics - Algebraic Topology

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2500 - 2532

Let A be a Koszul Calabi–Yau algebra. We show that there exists an isomorphism of Batalin–Vilkovisky algebras between the Hochschild cohomology ring of A and...

16E40 | 14A22 | 55U30 | 16S38 | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | CYCLIC HOMOLOGY | RING | DUALIZING COMPLEXES | Algebra

16E40 | 14A22 | 55U30 | 16S38 | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | CYCLIC HOMOLOGY | RING | DUALIZING COMPLEXES | Algebra

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 04/2019, Volume 69, Issue 2, pp. 425 - 432

Let and be Banach 𝔄-bimodule and Banach 𝔅-bimodule algebras, respectively. Also let be a Banach , -module and Banach 𝔄, 𝔅-module with compatible actions....

16E40 | Primary 46H20 | triangular Banach algebras | module amenability | weak amenability | module derivation | weak module amenability | Secondary 46H25 | MATHEMATICS

16E40 | Primary 46H20 | triangular Banach algebras | module amenability | weak amenability | module derivation | weak module amenability | Secondary 46H25 | MATHEMATICS

Journal Article

Selecta Mathematica, ISSN 1022-1824, 3/2018, Volume 24, Issue 1, pp. 531 - 561

Let R be the algebra of functions on a smooth affine irreducible curve S over a field k and let $${A_{\bullet }}$$ A∙ be a smooth and proper DG algebra over R....

16E40 | 14G17 | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | MODULES | Algebra

16E40 | 14G17 | Mathematics, general | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | MODULES | Algebra

Journal Article

Forum Mathematicum, ISSN 0933-7741, 03/2019, Volume 31, Issue 2, pp. 385 - 401

This paper presents a description of the fourth dimension quotient, using the theory of limits of functors from the category of free presentations of a given...

derived functor | 16E40 | 18G10 | dimension subgroup | 18A22 | 18G50 | Group ring | 20C07 | 20C05 | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | IDEALS | Quotients | Subgroups | Group theory

derived functor | 16E40 | 18G10 | dimension subgroup | 18A22 | 18G50 | Group ring | 20C07 | 20C05 | MATHEMATICS | MATHEMATICS, APPLIED | HOMOLOGY | IDEALS | Quotients | Subgroups | Group theory

Journal Article

Advances in Mathematics, ISSN 0001-8708, 10/2014, Volume 264, pp. 308 - 354

A skew Calabi–Yau algebra is a generalization of a Calabi–Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological...

Calabi–Yau algebra | Homological identity | Skew Calabi–Yau algebra | Nakayama automorphism | Homological determinant | Artin–Schelter regular | Artin–Schelter Gorenstein | Artin-Schelter regular | Artin-Schelter Gorenstein | Skew Calabi-Yau algebra | Calabi-Yau algebra | DIMENSION-3 | RINGS | CATEGORIES | DUALIZING COMPLEXES | FORMS | MATHEMATICS | SMASH PRODUCTS | GORENSTEINNESS | NOETHERIAN HOPF-ALGEBRAS | GRADED ALGEBRAS | Calabi-Yau-algebra | Algebra

Calabi–Yau algebra | Homological identity | Skew Calabi–Yau algebra | Nakayama automorphism | Homological determinant | Artin–Schelter regular | Artin–Schelter Gorenstein | Artin-Schelter regular | Artin-Schelter Gorenstein | Skew Calabi-Yau algebra | Calabi-Yau algebra | DIMENSION-3 | RINGS | CATEGORIES | DUALIZING COMPLEXES | FORMS | MATHEMATICS | SMASH PRODUCTS | GORENSTEINNESS | NOETHERIAN HOPF-ALGEBRAS | GRADED ALGEBRAS | Calabi-Yau-algebra | Algebra

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 9/2016, Volume 181, Issue 1, pp. 1 - 33

Let A be a unital associative algebra over a field k. All unital associative algebras containing A as a subalgebra of a given codimension $$\mathfrak {c}$$ c...

16E40 | Unified products | 16D70 | 16Z05 | Mathematics, general | Mathematics | Galois groups | Classification of algebras | LIE-ALGEBRAS | MATHEMATICS | HOPF-ALGEBRAS | CROSSED-PRODUCTS | Algebra

16E40 | Unified products | 16D70 | 16Z05 | Mathematics, general | Mathematics | Galois groups | Classification of algebras | LIE-ALGEBRAS | MATHEMATICS | HOPF-ALGEBRAS | CROSSED-PRODUCTS | Algebra

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 4/2019, Volume 14, Issue 2, pp. 395 - 420

This paper is devoted to study Frobenius Poisson algebras. We introduce pseudo-unimodular Poisson algebras by generalizing unimodular Poisson algebras, and...

Batalin-Vilkovisky algebra | 16E40 | modular derivation | 17B40 | 17B63 | Poisson (co)homology | Mathematics, general | Mathematics | Poisson algebra | Frobenius algebra | MATHEMATICS | Operators (mathematics) | Homology | Polynomials | Algebra | Mathematical analysis | Modular structures

Batalin-Vilkovisky algebra | 16E40 | modular derivation | 17B40 | 17B63 | Poisson (co)homology | Mathematics, general | Mathematics | Poisson algebra | Frobenius algebra | MATHEMATICS | Operators (mathematics) | Homology | Polynomials | Algebra | Mathematical analysis | Modular structures

Journal Article

Letters in Mathematical Physics, ISSN 0377-9017, 12/2017, Volume 107, Issue 12, pp. 2415 - 2432

We propose a simple injective resolution for the Hochschild complex of the Weyl algebra. By making use of this resolution, we derive explicit expressions for...

Geometry | Higher-spin theories | Primary 16E40 | Theoretical, Mathematical and Computational Physics | Complex Systems | Secondary 70S20 | Hochschild cohomology | Group Theory and Generalizations | Physics | Weyl algebra

Geometry | Higher-spin theories | Primary 16E40 | Theoretical, Mathematical and Computational Physics | Complex Systems | Secondary 70S20 | Hochschild cohomology | Group Theory and Generalizations | Physics | Weyl algebra

Journal Article

Proceedings of the London Mathematical Society, ISSN 0024-6115, 12/2017, Volume 115, Issue 6, pp. 1149 - 1169

We apply new techniques to compute Gerstenhaber brackets on the Hochschild cohomology of a skew group algebra formed from a polynomial ring and a finite group...

16E40 | 16S35 (primary) | MATHEMATICS | POISSON MANIFOLDS | ALGEBRAS | HOCHSCHILD COHOMOLOGY | PRODUCTS | DEFORMATIONS

16E40 | 16S35 (primary) | MATHEMATICS | POISSON MANIFOLDS | ALGEBRAS | HOCHSCHILD COHOMOLOGY | PRODUCTS | DEFORMATIONS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 5/2016, Volume 106, Issue 5, pp. 431 - 438

We discuss the notion of singular formal deformation in algebraic setup. Such deformations show up in both finite and infinite dimensional structures. It turns...

16E40 | 17B55 | Formal deformation | Mathematics, general | 17B70 | Singular deformation | Mathematics | 16S80 | 13D10 | 14B12 | Lie algebra | 14D15 | Algebra

16E40 | 17B55 | Formal deformation | Mathematics, general | 17B70 | Singular deformation | Mathematics | 16S80 | 13D10 | 14B12 | Lie algebra | 14D15 | Algebra

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2019, Volume 22, Issue 2, pp. 425 - 435

Let k be an algebraically closed field. For a graded algebra, Mori introduced a notion of cogeometric pair (E, σ), where E ⊂ ℙ n − 1 $E\subset \mathbb...

Self-injective Koszul algebras | 16W50 | Hochschild cohomology rings | Non-associative Rings and Algebras | Koszul dual | Commutative Rings and Algebras | 16E05 | Mathematics | 16E40 | Associative Rings and Algebras | AS-regular algebras | 16D50 | Cogeometric algebras | Geometric algebras | 16S37 | 16S38 | MATHEMATICS | MODULES | SUPPORT VARIETIES | Algebra

Self-injective Koszul algebras | 16W50 | Hochschild cohomology rings | Non-associative Rings and Algebras | Koszul dual | Commutative Rings and Algebras | 16E05 | Mathematics | 16E40 | Associative Rings and Algebras | AS-regular algebras | 16D50 | Cogeometric algebras | Geometric algebras | 16S37 | 16S38 | MATHEMATICS | MODULES | SUPPORT VARIETIES | Algebra

Journal Article

Journal of Homotopy and Related Structures, ISSN 2193-8407, 9/2016, Volume 11, Issue 3, pp. 425 - 441

We introduce BV-algebra structures on the homology of the space of framed long knots in $${\mathbb {R}}^n$$ R n in two ways. The first one is given in a...

Connes’ boundary operator | Algebraic Topology | BV algebra | Primary 55P50 | Secondary 16E40 | 57R40 | Mathematics | Hochschild homology | Algebra | Functional Analysis | Hatcher’s cycle | 57Q45 | Space of long knots | Number Theory | MATHEMATICS | Hatcher's cycle | COHOMOLOGY | Connes' boundary operator | CUBES

Connes’ boundary operator | Algebraic Topology | BV algebra | Primary 55P50 | Secondary 16E40 | 57R40 | Mathematics | Hochschild homology | Algebra | Functional Analysis | Hatcher’s cycle | 57Q45 | Space of long knots | Number Theory | MATHEMATICS | Hatcher's cycle | COHOMOLOGY | Connes' boundary operator | CUBES

Journal Article

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