Injective Hopf bimodules, cohomologies of infinite dimensional Hopf algebras and graded-commutativity of the Yoneda product.

DOI10.1016/J.JALGEBRA.2004.01.024zbMath1063.16048arXivmath/0207154OpenAlexW2091448201WikidataQ122224116 ScholiaQ122224116MaRDI QIDQ1883059

Rachel Taillefer

Publication date: 1 October 2004

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

Full work available at URL: https://arxiv.org/abs/math/0207154

zbMATH Keywords

Hopf algebrascohomologyGerstenhaber algebrascup-productHopf bimodulesYoneda productgraded Lie brackets

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Graded rings and modules (associative rings and algebras) (16W50) Hopf algebras (aspects of homology and homotopy of topological groups) (57T05)

Related Items (19)

Lie brackets on Hopf algebra cohomology ⋮ Cocyclic complexes of Hopf algebras with special antipodes ⋮ Bialgebra Cohomology of the Duals of a Class of Generalized Taft Algebras ⋮ Cyclic Gerstenhaber-Schack cohomology ⋮ On the monoidal invariance of the cohomological dimension of Hopf algebras ⋮ The Hilton-Heckmann argument for the anti-commutativity of cup products ⋮ G-structure on the cohomology of Hopf algebras ⋮ Formality theorem and bialgebra deformations ⋮ The Batalin-Vilkovisky structure over the Hochschild cohomology ring of a group algebra ⋮ Tetramodules over a bialgebra form a 2-fold monoidal category ⋮ Calabi–Yau property of quantum groups of GL(2) representation type ⋮ Differential graded categories and Deligne conjecture ⋮ Lie structure on Hopf algebra cohomology ⋮ Monoidal categories and the Gerstenhaber bracket in Hochschild cohomology ⋮ Hochschild homology of Hopf algebras and free Yetter–Drinfeld resolutions of the counit ⋮ Connes-Moscovici characteristic map is a Lie algebra morphism. ⋮ Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies ⋮ Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras. ⋮ Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids.

Cites Work

• Biinvertible actions of Hopf algebras
• Hopf bimodules are modules
• Cyclic homology of Hopf algebras
• Differential calculus on compact matrix pseudogroups (quantum groups)
• The cohomology structure of an associative ring
• Bialgebra cohomology, deformations, and quantum groups.
• An exact sequence interpretation of the Lie bracket in Hochschild cohomology
• DEFORMATION COHOMOLOGY FOR YETTER-DRINFEL'D MODULES AND HOPF (BI)MODUL ES
• G-structure on the cohomology of Hopf algebras
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