Homology, Homotopy and Applications
Volume 9 (2007)
Hopf-Hochschild (co)homology of module algebras
Pages: 451 – 472
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.
Hochschild cohomology; module algebra; Hopf algebra; bialgebra; Morita invariance
2010 Mathematics Subject Classification