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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 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.

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Atabey Kaygun. 2006-08-24. Hopf--Hochschild (co)homology of module algebras. https://arxiv.org/abs/math/0606340

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