Homology, Homotopy and Applications

Hopf-Hochschild (co)homology of module algebras

Atabey Kaygun

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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.

Article information

Source
Homology Homotopy Appl., Volume 9, Number 2 (2007), 451-472.

Dates
First available in Project Euclid: 23 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.hha/1201127346

Mathematical Reviews number (MathSciNet)
MR2366958

Zentralblatt MATH identifier
1130.16009

Subjects
Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)

Keywords
Hochschild cohomology module algebra Hopf algebra bialgebra Morita invariance

Citation

Kaygun, Atabey. Hopf-Hochschild (co)homology of module algebras. Homology Homotopy Appl. 9 (2007), no. 2, 451--472. https://projecteuclid.org/euclid.hha/1201127346


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