Operations on the Hopf-Hochschild complex for module-algebras.

DOI10.4310/HHA.2011.V13.N1.A10zbMATH Open1243.16007arXivmath/0607629MaRDI QIDQ542642

Donald Yau

Publication date: 10 June 2011

Published in: Homology, Homotopy and Applications (Search for Journal in Brave)

Abstract: It is observed that Kaygun's Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, (i) an analogue of Deligne's Conjecture holds for module-algebras, and (ii) the Hopf-Hochschild cohomology of a module-algebra has a Gerstenhaber algebra structure.

Full work available at URL: https://arxiv.org/abs/math/0607629

zbMATH Keywords

bialgebrasGerstenhaber algebrasbrace algebrasDeligne conjectureHopf-Hochschild cochain complexesHopf-Hochschild cohomology modulesmodule-algebras

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Homological methods in Lie (super)algebras (17B55) Deformations of associative rings (16S80) Nonassociative algebras satisfying other identities (17A30) Bialgebras (16T10)

Related Items (3)

On Hopf algebra structures over free operads. ⋮ Higher operations on the Hochschild complex ⋮ The fundamental theorem of Hopf modules for Hopf braces

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