Gerstenhaber–Schack cohomology for Hom-bialgebras and deformations

DOI10.1080/00927872.2016.1265124zbMath1393.16025arXiv1608.02084OpenAlexW2963542221MaRDI QIDQ4977695

Abdenacer Makhlouf, Khadra Dekkar

Publication date: 16 August 2017

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1608.02084

zbMATH Keywords

cohomologydeformationHom-Hopf algebraHom-bialgebra

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Deformations of associative rings (16S80) Formal methods and deformations in algebraic geometry (14D15) Bialgebras (16T10)

Related Items

$\alpha$-type Hochschild cohomology of Hom-associative algebras and Hom-bialgebras ⋮ Central invariants and enveloping algebras of braided Hom-Lie algebras ⋮ Drinfeld codoubles of Hom-Hopf algebras ⋮ α-TYPE CHEVALLEY–EILENBERG COHOMOLOGY OF HOM-LIE ALGEBRAS AND BIALGEBRAS

Cites Work

• Unnamed Item
• Unnamed Item
• \(q\)-deformation of the Virasoro algebra with central extension
• Hom-L-R-smash products, Hom-diagonal crossed products and the Drinfeld double of a Hom-Hopf algebra.
• On hom-algebras with surjective twisting
• Hom-Lie superalgebras and Hom-Lie admissible superalgebras
• Representations of hom-Lie algebras
• Bialgebra cohomology, pointed Hopf algebras, and deformations.
• Cohomology theories of Hopf bimodules and cup-product.
• The deformation complex for differential graded Hopf algebras
• Deformations of Lie algebras using \(\sigma\)-derivations
• The cohomology structure of an associative ring
• Quasi-hom-Lie algebras, central extensions and 2-cocycle-like identities
• Hom-algebra structures
• On the deformation of rings and algebras
• On the cohomology groups of an associative algebra
• Unital algebras of Hom-associative type and surjective or injective twistings
• Monoidal Hom–Hopf Algebras
• Hom-quantum groups: I. Quasi-triangular Hom-bialgebras
• Lazy 2-cocycles over monoidal Hom-Hopf algebras
• A THEOREM ON STABILITY OF COMPLEX STRUCTURES
• Bialgebra cohomology, deformations, and quantum groups.
• Notes on 1-parameter formal deformations of Hom-associative and Hom-Lie algebras
• Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras
• HOM-ALGEBRAS AND HOM-COALGEBRAS
• The Hom–Yang–Baxter equation and Hom–Lie algebras
• On Graded Bialgebra Deformations
• Integrals for monoidal Hom-Hopf algebras and their applications
• Yetter-Drinfeld modules for Hom-bialgebras