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.
Original language | English |
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Pages (from-to) | 451-472 |
Number of pages | 22 |
Journal | Homology, Homotopy and Applications |
Volume | 9 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2007 |
Externally published | Yes |
Keywords
- Bialgebra
- Hochschild cohomology
- Hopf algebra
- Module algebra
- Morita invariance