Acta Mathematica Hungarica, ISSN 0236-5294, 2/2018, Volume 154, Issue 1, pp. 223 - 230

We generalize [4, Theorem 4.3] to the case of Hopf–Galois extension, by introducing the cotensor product of a comodule algebra and its opposite algebra, and...

Hopf–Galois extension | Mathematics, general | Hochschild cohomology | Mathematics | 16W30 | cotensor product | MATHEMATICS | Hopf-Galois extension | ALGEBRAS | Algebra

Hopf–Galois extension | Mathematics, general | Hochschild cohomology | Mathematics | 16W30 | cotensor product | MATHEMATICS | Hopf-Galois extension | ALGEBRAS | 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

Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2017, Volume 145, Issue 4, pp. 1475 - 1480

We prove that if an algebra is either selfinjective, local or graded, then the Hochschild homology dimension of its trivial extension is infinite.

Hochschild homology | Trivial extensions | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL DIMENSION

Hochschild homology | Trivial extensions | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL DIMENSION

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 07/2016, Volume 220, Issue 7, pp. 2471 - 2499

Let B be the split extension of a finite dimensional algebra C by a C-C-bimodule E. We define a morphism of associative graded algebras φ⁎:HH⁎(B)→HH⁎(C) from...

MATHEMATICS | MATHEMATICS, APPLIED | QUIVERS | RESOLUTIONS | RING | TRIVIAL EXTENSIONS | A(N) | CLUSTER-TILTED ALGEBRAS | Algebra | Mathematics | Representation Theory

MATHEMATICS | MATHEMATICS, APPLIED | QUIVERS | RESOLUTIONS | RING | TRIVIAL EXTENSIONS | A(N) | CLUSTER-TILTED ALGEBRAS | Algebra | Mathematics | Representation Theory

Journal Article

Communications in Algebra, ISSN 0092-7872, 12/2018, Volume 46, Issue 12, pp. 5273 - 5282

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.

16E40 | partial relation extension | Hochschild cohomology groups | 16G20 | Hochschild projection morphisms | MATHEMATICS | MODULES | CLUSTER-TILTED ALGEBRAS | Homology

16E40 | partial relation extension | Hochschild cohomology groups | 16G20 | Hochschild projection morphisms | MATHEMATICS | MODULES | CLUSTER-TILTED ALGEBRAS | Homology

Journal Article

Journal of Pure and Applied Algebra, ISSN 0022-4049, 11/2015, Volume 219, Issue 11, pp. 4953 - 4997

We concretely construct a 2-categorically extended TQFT that extends the Reshetikhin–Turaev TQFT to cobordisms with corners. The source category will be a well...

QUANTUM-FIELD THEORIES | MATHEMATICS | MATHEMATICS, APPLIED | HOCHSCHILD CO-CHAINS | MODULI SPACE ACTIONS

QUANTUM-FIELD THEORIES | MATHEMATICS | MATHEMATICS, APPLIED | HOCHSCHILD CO-CHAINS | MODULI SPACE ACTIONS

Journal Article

7.
Full Text
The ordinary quivers of Hochschild extension algebras for self-injective Nakayama algebras

Communications in Algebra, ISSN 0092-7872, 09/2018, Volume 46, Issue 9, pp. 3950 - 3964

Let T be a Hochschild extension algebra of a finite dimensional algebra A over a field K by the standard duality A-bimodule Hom K (A, K). In this paper, we...

16E40 | trivial extension | Hochschild extension | self-injective Nakayama algebra | quiver | 16G20 | symmetric algebra | 16L60 | Hochschild (co)homology | MATHEMATICS | COHOMOLOGY | HOMOLOGY | Homology | Algebra

16E40 | trivial extension | Hochschild extension | self-injective Nakayama algebra | quiver | 16G20 | symmetric algebra | 16L60 | Hochschild (co)homology | MATHEMATICS | COHOMOLOGY | HOMOLOGY | Homology | Algebra

Journal Article

Bulletin of the Iranian Mathematical Society, ISSN 1017-060X, 6/2018, Volume 44, Issue 3, pp. 749 - 762

In this paper, we will describe the general form of commuting mappings of Hochschild extension algebras and characterize the properness of commuting mappings...

Secondary 16W25 | Commuting mapping | 46H40 | Hochschild extension | Mathematics, general | Mathematics | Primary 15A78 | Triangular algebra | MATHEMATICS | MAPS | TRACES | DERIVATIONS

Secondary 16W25 | Commuting mapping | 46H40 | Hochschild extension | Mathematics, general | Mathematics | Primary 15A78 | Triangular algebra | MATHEMATICS | MAPS | TRACES | DERIVATIONS

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 05/2018, Volume 17, Issue 5

Let k be a commutative algebra with Q subset of k and let (E,p,i) be a cleft extension of A. We obtain a new mixed complex, simpler than the canonical one,...

Cleft extensions | Cyclic homology | Hochschild homology | MATHEMATICS | MATHEMATICS, APPLIED

Cleft extensions | Cyclic homology | Hochschild homology | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Algebraic and Geometric Topology, ISSN 1472-2747, 03/2017, Volume 17, Issue 2, pp. 693 - 704

We treat the question of base-change in THH for faithful Galois extensions of ring spectra in the sense of Rognes. Given a faithful Galois extension A -> B of...

Galois extensions | Structured ring spectra | Topological Hochschild homology | MATHEMATICS | HOCHSCHILD | CYCLIC HOMOLOGY

Galois extensions | Structured ring spectra | Topological Hochschild homology | MATHEMATICS | HOCHSCHILD | CYCLIC HOMOLOGY

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 05/2017, Volume 65, Issue 5, pp. 1022 - 1034

Let be a field and Q a finite simply laced quiver without oriented cycles. Firstly, we prove that each Lie derivation of the generalized one-point extension of...

Lie derivation | 16E40 | 16W25 | generalized one-point extension | 16G10 | Hochschild (co)homology | MATHEMATICS | Hochschild (co) homology | RING | Algebra | Mathematical analysis | Images | Derivation | Homology | Decomposition | Standards | Rings (mathematics)

Lie derivation | 16E40 | 16W25 | generalized one-point extension | 16G10 | Hochschild (co)homology | MATHEMATICS | Hochschild (co) homology | RING | Algebra | Mathematical analysis | Images | Derivation | Homology | Decomposition | Standards | Rings (mathematics)

Journal Article

Journal of Noncommutative Geometry, ISSN 1661-6952, 2014, Volume 8, Issue 2, pp. 587 - 609

Suppose that E = A[x; sigma, delta] is an Ore extension with sigma an automorphism. It is proved that if A is twisted Calabi-Yau of dimension d, then E is...

Ore extension | Twisted Calabi-Yau algebra | Nakayama automorphism | Artin-Schelter regular algebra | MATHEMATICS | MATHEMATICS, APPLIED | twisted Calabi-Yau algebra | ENVELOPING-ALGEBRAS | RIGID DUALIZING COMPLEX | HOCHSCHILD | PHYSICS, MATHEMATICAL

Ore extension | Twisted Calabi-Yau algebra | Nakayama automorphism | Artin-Schelter regular algebra | MATHEMATICS | MATHEMATICS, APPLIED | twisted Calabi-Yau algebra | ENVELOPING-ALGEBRAS | RIGID DUALIZING COMPLEX | HOCHSCHILD | PHYSICS, MATHEMATICAL

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 08/2016, Volume 11, Issue 4, pp. 869 - 900

We study structures of Hochschild 2-cocycles related to endomorphisms and introduce a skew Hochschild 2-cocycle. We moreover define skew Hochschild extensions...

matrix rings | skew triangular matrix rings | Skew Hochschild extensions | (uniquely) clean rings | symmetric rings | MATHEMATICS | Studies | Theorems | Mathematical models | Mathematics | Algebra | Cleaning | Mathematical analysis | Symmetry | Rings (mathematics)

matrix rings | skew triangular matrix rings | Skew Hochschild extensions | (uniquely) clean rings | symmetric rings | MATHEMATICS | Studies | Theorems | Mathematical models | Mathematics | Algebra | Cleaning | Mathematical analysis | Symmetry | Rings (mathematics)

Journal Article

Frontiers of Mathematics in China, ISSN 1673-3452, 08/2016, Volume 11, Issue 4, pp. 1003 - 1015

We consider a one point extension algebra B of a quiver algebra A(q) over a field k defined by two cycles and a quantum-like relation depending on a nonzero...

Hochschild cohomology | quantum-like relation | one point extension | MATHEMATICS | SUPPORT VARIETIES | Studies | Theorems | Mathematical models | Mathematics | Algebra | Unity | Mathematical analysis | Roots | Rings (mathematics)

Hochschild cohomology | quantum-like relation | one point extension | MATHEMATICS | SUPPORT VARIETIES | Studies | Theorems | Mathematical models | Mathematics | Algebra | Unity | Mathematical analysis | Roots | Rings (mathematics)

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2016, Volume 283, Issue 1, pp. 223 - 255

We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive...

Hochschild cohomology | Quantum symmetric algebra | Gerstenhaber bracket | Skew group algebra | quantum symmetric algebra | MATHEMATICS | skew group algebra | RINGS | SUPPORT VARIETIES

Hochschild cohomology | Quantum symmetric algebra | Gerstenhaber bracket | Skew group algebra | quantum symmetric algebra | MATHEMATICS | skew group algebra | RINGS | SUPPORT VARIETIES

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 04/2016, Volume 15, Issue 3

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first...

quantum symmetric algebra | Hochschild cohomology | skew group algebra | color Lie algebra | Gerstenhaber bracket | Quantum Drinfeld orbifold algebra | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | DRINFELD ORBIFOLD ALGEBRAS | HECKE ALGEBRAS | BIRKHOFF-WITT THEOREM

quantum symmetric algebra | Hochschild cohomology | skew group algebra | color Lie algebra | Gerstenhaber bracket | Quantum Drinfeld orbifold algebra | MATHEMATICS | MATHEMATICS, APPLIED | COHOMOLOGY | DRINFELD ORBIFOLD ALGEBRAS | HECKE ALGEBRAS | BIRKHOFF-WITT THEOREM

Journal Article

Linear and Multilinear Algebra, ISSN 0308-1087, 06/2018, Volume 66, Issue 6, pp. 1133 - 1152

The notion of non-abelian Hom-Leibniz tensor product is introduced and some properties are established. This tensor product is used in the description of the...

17B55 | 17A30 | non-abelian tensor product | central extension | 18G60 | Hochschild homology | 17B60 | universal | Hom-Leibniz algebra | Hom-associative algebra | 18G35 | Hom–Leibniz algebra | universal -central extension | LIE-ALGEBRAS | MATHEMATICS | DEFORMATIONS | universal (alpha)-central extension | Homology

17B55 | 17A30 | non-abelian tensor product | central extension | 18G60 | Hochschild homology | 17B60 | universal | Hom-Leibniz algebra | Hom-associative algebra | 18G35 | Hom–Leibniz algebra | universal -central extension | LIE-ALGEBRAS | MATHEMATICS | DEFORMATIONS | universal (alpha)-central extension | Homology

Journal Article

Journal of Algebra, ISSN 0021-8693, 2011, Volume 332, Issue 1, pp. 366 - 385

We introduce characteristic classes for the spectral sequence associated to a split short exact sequence of Hopf algebras. These classes can be seen as...

(Lyndon–)Hochschild–Serre spectral sequence | Hopf algebra cohomology | Characteristic classes | (Lyndon-)Hochschild-Serre spectral sequence | MATHEMATICS

(Lyndon–)Hochschild–Serre spectral sequence | Hopf algebra cohomology | Characteristic classes | (Lyndon-)Hochschild-Serre spectral sequence | MATHEMATICS

Journal Article

Advances in Mathematics, ISSN 0001-8708, 02/2007, Volume 209, Issue 1, pp. 381 - 405

We calculate Ext (k) (Δ (λ), Δ (μ)), Ext (k) (L (λ), Δ (μ)), Ext (k) (Δ (λ), L (μ)), Ext (k) (L (λ), L (μ)), where Δ (λ) is the Weyl module of highest weight...

Lyndon-Hochschild-Serre spectral sequence | Cohomology | Special linear group | Ext groups | MATHEMATICS | special linear group | cohomology | WEYL MODULES

Lyndon-Hochschild-Serre spectral sequence | Cohomology | Special linear group | Ext groups | MATHEMATICS | special linear group | cohomology | WEYL MODULES

Journal Article

Journal of Algebra, ISSN 0021-8693, 2007, Volume 315, Issue 2, pp. 852 - 873

In this article we prove derived invariance of Hochschild–Mitchell homology and cohomology and we extend to k-linear categories a result by Barot and Lenzing...

One-point extension | k-Category | Hochschild–Mitchell cohomology | Derived equivalence | Hochschild-Mitchell cohomology | GALOIS COVERINGS | MATHEMATICS | derived equivalence | COHOMOLOGY | one-point extension | k-category | CATEGORIES | EQUIVALENCE | K-Theory and Homology | Mathematics

One-point extension | k-Category | Hochschild–Mitchell cohomology | Derived equivalence | Hochschild-Mitchell cohomology | GALOIS COVERINGS | MATHEMATICS | derived equivalence | COHOMOLOGY | one-point extension | k-category | CATEGORIES | EQUIVALENCE | K-Theory and Homology | Mathematics

Journal Article

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