Homology, Homotopy and Applications

Volume 9 (2007)

Number 2

Hopf-Hochschild (co)homology of module algebras

Pages: 451 – 472

DOI: https://dx.doi.org/10.4310/HHA.2007.v9.n2.a17

Author

Atabey Kaygun (Department of Mathematics, The Ohio State University, Columbus, Oh., U.S.A.)

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.

Keywords

Hochschild cohomology, module algebra, Hopf algebra, bialgebra, Morita invariance

2010 Mathematics Subject Classification

16E40

Published 1 January 2007