Journal of Algebra, ISSN 0021-8693, 06/2018, Volume 504, pp. 536 - 567

We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve...

Smash product algebras | Hopf algebras | PBW deformations

Smash product algebras | Hopf algebras | PBW deformations

Journal Article

JOURNAL OF ALGEBRA, ISSN 0021-8693, 06/2018, Volume 504, pp. 536 - 567

We present new examples of deformations of smash product algebras that arise from Hopf algebra actions on pairs of module algebras. These examples involve...

MATHEMATICS | Smash product algebras | PBW deformations | HOPF-ALGEBRAS | W-ALGEBRAS | HECKE ALGEBRAS | Hopf algebras | RATIONAL CHEREDNIK ALGEBRAS

MATHEMATICS | Smash product algebras | PBW deformations | HOPF-ALGEBRAS | W-ALGEBRAS | HECKE ALGEBRAS | Hopf algebras | RATIONAL CHEREDNIK ALGEBRAS

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2017, Volume 482, pp. 204 - 223

We define the partial group cohomology as the right derived functor of the functor of partial invariants, we relate this cohomology with partial derivations...

Partial smash products | Spectral sequence | Cohomology | Partial actions | MATHEMATICS | ALGEBRAS | GALOIS THEORY | CROSSED-PRODUCTS | Algebra | Mathematics - Rings and Algebras

Partial smash products | Spectral sequence | Cohomology | Partial actions | MATHEMATICS | ALGEBRAS | GALOIS THEORY | CROSSED-PRODUCTS | Algebra | Mathematics - Rings and Algebras

Journal Article

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Full Text
Semidirect products of weak multiplier Hopf algebras: Smash products and smash coproducts

Communications in Algebra, ISSN 0092-7872, 08/2018, Volume 46, Issue 8, pp. 3241 - 3261

In this paper, we will develop the smash product of weak multiplier Hopf algebras unifying the cases of Hopf algebras, weak Hopf algebras and multiplier Hopf...

16T05 | weak multiplier Hopf algebra | Actions | 16S40 | smash products | MATHEMATICS | DUALITY | CROSSED-PRODUCTS | BIALGEBRAS | Integrals | Algebra

16T05 | weak multiplier Hopf algebra | Actions | 16S40 | smash products | MATHEMATICS | DUALITY | CROSSED-PRODUCTS | BIALGEBRAS | Integrals | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2015, Volume 441, pp. 314 - 343

We introduce the Hom-analogue of the L-R-smash product and use it to define the Hom-analogue of the diagonal crossed product. When is a finite dimensional...

Hom-bialgebra | Hom-Hopf algebra | L-R-smash product | Twisted tensor product | Twisting operator | Drinfeld double | Hom-associative algebra | QUANTUM GROUPS | UNIVERSAL DEFORMATION FORMULAS | VIRASORO ALGEBRA | LIE-ALGEBRAS | MATHEMATICS | CENTRAL EXTENSION | QUANTIZATION | HOMOLOGY | TWISTED TENSOR-PRODUCTS | Algebra

Hom-bialgebra | Hom-Hopf algebra | L-R-smash product | Twisted tensor product | Twisting operator | Drinfeld double | Hom-associative algebra | QUANTUM GROUPS | UNIVERSAL DEFORMATION FORMULAS | VIRASORO ALGEBRA | LIE-ALGEBRAS | MATHEMATICS | CENTRAL EXTENSION | QUANTIZATION | HOMOLOGY | TWISTED TENSOR-PRODUCTS | Algebra

Journal Article

Journal of Algebra and its Applications, ISSN 0219-4988, 2014, Volume 13, Issue 7, pp. 1450036 - 1-1450036-14

We define a "mirror version" of Brzezinski's crossed product and we prove that, under certain circumstances, a Brzezinski's crossed product D circle times...

twisted tensor product of algebras | Crossed product | quasi-Hopf smash product | MATHEMATICS | SMASH PRODUCTS | MATHEMATICS, APPLIED | ALGEBRAS | TWISTED TENSOR-PRODUCTS | Construction | Tensors | Algebra | Mathematical analysis

twisted tensor product of algebras | Crossed product | quasi-Hopf smash product | MATHEMATICS | SMASH PRODUCTS | MATHEMATICS, APPLIED | ALGEBRAS | TWISTED TENSOR-PRODUCTS | Construction | Tensors | Algebra | Mathematical analysis

Journal Article

2017, Mathematical surveys and monographs, ISBN 1470437856, Volume 224, vi, 321 pages

Associative rings and algebras -- Rings and algebras arising under various constructions -- Twisted and skew group rings, crossed products | C-algebras | Associative rings and algebras -- Rings and algebras arising under various constructions -- Smash products of general Hopf actions | Functional analysis -- Selfadjoint operator algebras ($C^$-algebras, von Neumann ($W^$-) algebras, etc.) -- Decomposition theory for $C^$-algebras | Banach spaces | Isometrics (Mathematics) | Isométrie (mathématiques) | C-algèbres | Functional analysis -- Selfadjoint operator algebras ($C^$-algebras, von Neumann ($W^$-) algebras, etc.) -- Noncommutative dynamical systems | Banach, Espaces de

Book

Communications in Algebra, ISSN 0092-7872, 02/2019, Volume 47, Issue 2, pp. 585 - 610

Let be a field, G a group, and (Q, I) a bound quiver. A map is called a G-weight on Q, which defines a G-graded -category , and W is called homogeneous if I is...

16W50 | Coverings | Brauer graphs | gradings | quiver presentations | smash products | 18D05 | 16W22 | MATHEMATICS | ALGEBRAS | GALOIS COVERING FUNCTORS | EQUIVALENCE CLASSIFICATION | Permutations | Graphs | Computation | Weight | Group theory

16W50 | Coverings | Brauer graphs | gradings | quiver presentations | smash products | 18D05 | 16W22 | MATHEMATICS | ALGEBRAS | GALOIS COVERING FUNCTORS | EQUIVALENCE CLASSIFICATION | Permutations | Graphs | Computation | Weight | Group theory

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2014, Volume 42, Issue 10, pp. 4204 - 4234

We consider two new algebras from an H-biquasimodule algebra A and a Hopf quasigroup H: twisted smash product A ⊛ H and L-R smash product A⋇H, and find...

Hopf quasigroup | L-R smash product | Twisted smash product | Twist double | MATHEMATICS | BIMODULE ALGEBRAS | Algebra

Hopf quasigroup | L-R smash product | Twisted smash product | Twist double | MATHEMATICS | BIMODULE ALGEBRAS | Algebra

Journal Article

Communications in Algebra, ISSN 0092-7872, 10/2016, Volume 44, Issue 10, pp. 4140 - 4164

Let (H, α) be a monoidal Hom-Hopf algebra and (A, β) be an (H, α)-Hom-bimodule algebra. In this article, we first introduce the notion of a twisted Hom-smash...

Monoidal Hom-Hopf algebra | Morita context | 16S40 | Twisted Hom-smash product | Maschke-type theorem | MATHEMATICS | Theorems | Algebra | Categories | Images

Monoidal Hom-Hopf algebra | Morita context | 16S40 | Twisted Hom-smash product | Maschke-type theorem | MATHEMATICS | Theorems | Algebra | Categories | Images

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 8/2019, Volume 22, Issue 4, pp. 785 - 799

A general criterion is given for when the center of a Taft algebra smash product is the fixed ring. This is applied to the study of the noncommutative...

Discriminant | Azumaya locus | Non-associative Rings and Algebras | 16S40 | Commutative Rings and Algebras | Mathematics | Automorphism group | Smash product | 11R29 | Ore extension | Associative Rings and Algebras | Poisson algebra | Taft algebra | 16W20 | 16S36 | 16W22 | MATHEMATICS | AUTOMORPHISM-GROUPS | POISSON | ANALOGS | PRIME IDEALS | Algebra | Automorphisms

Discriminant | Azumaya locus | Non-associative Rings and Algebras | 16S40 | Commutative Rings and Algebras | Mathematics | Automorphism group | Smash product | 11R29 | Ore extension | Associative Rings and Algebras | Poisson algebra | Taft algebra | 16W20 | 16S36 | 16W22 | MATHEMATICS | AUTOMORPHISM-GROUPS | POISSON | ANALOGS | PRIME IDEALS | Algebra | Automorphisms

Journal Article

Advances in Applied Clifford Algebras, ISSN 0188-7009, 9/2017, Volume 27, Issue 3, pp. 2885 - 2897

Let A be a finite dimensional algebra graded by a finite group, and let $$\Gamma $$ Γ be the corresponding smash product. We prove that if A is separably...

Stable module category | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Oppermann dimension | Applications of Mathematics | Physics, general | Secondary 16S34 | Physics | Primary 16G10 | 16P90 | Representation dimension | Smash product | MATHEMATICS, APPLIED | SELF-INJECTIVE ALGEBRAS | SKEW GROUP-ALGEBRAS | PHYSICS, MATHEMATICAL | Algebra

Stable module category | Mathematical Methods in Physics | Theoretical, Mathematical and Computational Physics | Oppermann dimension | Applications of Mathematics | Physics, general | Secondary 16S34 | Physics | Primary 16G10 | 16P90 | Representation dimension | Smash product | MATHEMATICS, APPLIED | SELF-INJECTIVE ALGEBRAS | SKEW GROUP-ALGEBRAS | PHYSICS, MATHEMATICAL | Algebra

Journal Article

Publicationes Mathematicae, ISSN 0033-3883, 2016, Volume 89, Issue 1-2, pp. 23 - 41

In this paper we first give the sufficient conditions under which a partial twisted smash product algebra and the usual tensor product coalgebra become a...

Partial twisted smash product | Frobenius | Partial representation | MATHEMATICS | partial twisted smash product | HOPF-ALGEBRAS | GALOIS THEORY | (CO)ACTIONS | partial representation | ENVELOPING ACTIONS

Partial twisted smash product | Frobenius | Partial representation | MATHEMATICS | partial twisted smash product | HOPF-ALGEBRAS | GALOIS THEORY | (CO)ACTIONS | partial representation | ENVELOPING ACTIONS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 08/2012, Volume 364, Issue 8, pp. 4155 - 4168

. Finally, we deduce from this Kharchenko's theorem on differential identities.]]>

Homomorphisms | Algebra | Mathematical theorems | Applied mathematics | Words | Differentials | Mathematical rings | Mathematics | Polynomials | Commuting | Centralizers | Universal enveloping algebras | Derivations | Differential identities | Smash products | Ore extensions | MATHEMATICS | differential identities | universal enveloping algebras | centralizers | smash products

Homomorphisms | Algebra | Mathematical theorems | Applied mathematics | Words | Differentials | Mathematical rings | Mathematics | Polynomials | Commuting | Centralizers | Universal enveloping algebras | Derivations | Differential identities | Smash products | Ore extensions | MATHEMATICS | differential identities | universal enveloping algebras | centralizers | smash products

Journal Article

Journal of Algebra, ISSN 0021-8693, 11/2016, Volume 465, pp. 62 - 80

We investigate Frobenius algebras and symmetric algebras in the monoidal category of right comodules over a Hopf algebra ; for the symmetric property is...

Symmetric algebra | Monoidal category | Hopf algebra | Frobenius algebra | Comodule | Smash product | MATHEMATICS | HOPF-ALGEBRAS | MONOIDAL CATEGORIES | FROBENIUS ALGEBRAS | Computer science | Algebra

Symmetric algebra | Monoidal category | Hopf algebra | Frobenius algebra | Comodule | Smash product | MATHEMATICS | HOPF-ALGEBRAS | MONOIDAL CATEGORIES | FROBENIUS ALGEBRAS | Computer science | Algebra

Journal Article

Journal of Algebra, ISSN 0021-8693, 07/2019, Volume 530, pp. 402 - 428

The smash product # of a Hopf algebra and an -module vertex operator algebra are investigated. -theory and contragredient module theory are founded for # . If...

Quantum vertex algebras | Vertex operator algebras | Hopf algebras | Smash product

Quantum vertex algebras | Vertex operator algebras | Hopf algebras | Smash product

Journal Article

Colloquium Mathematicum, ISSN 0010-1354, 2016, Volume 142, Issue 1, pp. 51 - 60

If A circle times(R,sigma) V and A circle times(P,nu) W are two Brzezinski crossed products and Q : W circle times V -> V circle times W is a linear map...

Twisted tensor product | Brzeziński crossed product | MATHEMATICS | SMASH PRODUCTS | twisted tensor product | ALGEBRAS | Brzezinski crossed product

Twisted tensor product | Brzeziński crossed product | MATHEMATICS | SMASH PRODUCTS | twisted tensor product | ALGEBRAS | Brzezinski crossed product

Journal Article

Algebra Colloquium, ISSN 1005-3867, 03/2014, Volume 21, Issue 1, pp. 129 - 146

We introduce a common generalization of the L-R-smash product and twisted tensor product of algebras, under the name L-R-twisted tensor product of algebras. We...

twisted tensor product | Hopf algebra | L-R-twisted tensor product | L-R-smash product | MATHEMATICS | MATHEMATICS, APPLIED | DIAGONAL CROSSED-PRODUCTS | LIE-GROUPS | QUANTUM GROUPS | UNIVERSAL DEFORMATION FORMULAS

twisted tensor product | Hopf algebra | L-R-twisted tensor product | L-R-smash product | MATHEMATICS | MATHEMATICS, APPLIED | DIAGONAL CROSSED-PRODUCTS | LIE-GROUPS | QUANTUM GROUPS | UNIVERSAL DEFORMATION FORMULAS

Journal Article

Algebras and Representation Theory, ISSN 1386-923X, 4/2018, Volume 21, Issue 2, pp. 259 - 276

We explore questions of projectivity and tensor products of modules for finite dimensional Hopf algebras. We construct many classes of examples in which tensor...

18D10 | Support varieties | Associative Rings and Algebras | Projective modules | Non-associative Rings and Algebras | 16T05 | Commutative Rings and Algebras | Mathematics | Nonsemisimple Hopf algebra | Smash coproduct | MATHEMATICS | MODULES | ELEMENTARY ABELIAN-GROUPS | EXAMPLES | Algebra | Modules

18D10 | Support varieties | Associative Rings and Algebras | Projective modules | Non-associative Rings and Algebras | 16T05 | Commutative Rings and Algebras | Mathematics | Nonsemisimple Hopf algebra | Smash coproduct | MATHEMATICS | MODULES | ELEMENTARY ABELIAN-GROUPS | EXAMPLES | Algebra | Modules

Journal Article

Algebra Colloquium, ISSN 1005-3867, 03/2018, Volume 25, Issue 1, pp. 1 - 30

In this paper we discuss about the semiprimitivity and the semiprimality of partial smash products. Let H be a semisimple Hopf algebra over a field k and let A...

semiprimitivity | partial (A, H)-module | partial smash product | Partial Hopf action | H-radical | semiprimality | partial Hopf action | MATHEMATICS, APPLIED | GALOIS THEORY | (CO)ACTIONS | RINGS | ENVELOPING ACTIONS | MATHEMATICS | HOPF MODULE ALGEBRAS | RADICALS | PARTIAL REPRESENTATIONS

semiprimitivity | partial (A, H)-module | partial smash product | Partial Hopf action | H-radical | semiprimality | partial Hopf action | MATHEMATICS, APPLIED | GALOIS THEORY | (CO)ACTIONS | RINGS | ENVELOPING ACTIONS | MATHEMATICS | HOPF MODULE ALGEBRAS | RADICALS | PARTIAL REPRESENTATIONS

Journal Article

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