Hopf-Hochschild (co)homology of module algebras

Atabey Kaygun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

We define a version of Hochschild homology and cohomology suitable for a class of algebras admitting compatible actions of bialgebras, called module algebras. We show that this (co)homology, called Hopf-Hochschild (co)homology, can also be defined as a derived functor on the category of representations of an equivariant analogue of the enveloping algebra of a crossed product algebra. We investigate the relationship of our theory with Hopf cyclic cohomology and also prove Morita invariance of the Hopf-Hochschild (co) homology.

Original languageEnglish
Pages (from-to)451-472
Number of pages22
JournalHomology, Homotopy and Applications
Volume9
Issue number2
DOIs
Publication statusPublished - 2007
Externally publishedYes

Keywords

  • Bialgebra
  • Hochschild cohomology
  • Hopf algebra
  • Module algebra
  • Morita invariance

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