Hopf--Hochschild (co)homology of module algebras

2006/06/14 by Atabey Kaygun, Kaygun, Atabey
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.KT #math.RA

paper · pdf · doi:10.48550/arxiv.math/0606340

19 Pages. Theorem 3.7 and Corollary 4.4 modified

arxiv created 2006/08/24 · arxiv updated 2009/12/01

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 this (co)homology, called Hopf--Hochschild (co)homology, can also be defined as a derived functor on the category of representations 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.

Related

• Hochschild (co)homology of Hopf crossed products
• Morita invariance of equivariant and Hopf-cyclic cohomology of module algebras over Hopf algebroids
• Hopf-cyclic homology and cohomology with coefficients
• The universal Hopf cyclic theory
• Cyclic Homology of Hopf Comodule Algebras and Hopf Module Coalgebras