Cohomology of Hopf Bimodules and Cup-product
Quantum Algebra
2009-10-31 v2
Abstract
Given a Hopf algebra A, there exist various cohomology theories for the category of Hopf bimodules over A, introduced by M. Gerstenhaber and S.D. Schack, and by C. Ospel. We prove, when A is finite dimensional, that they are equal to the Ext functor on the module category of an associative algebra associated to A, described by C. Cibils and M. Rosso. We also give an expression for a cup-product in the cohomology defined by C. Ospel, and prove that it corresponds to the Yoneda product of extensions.
Cite
@article{arxiv.math/0005019,
title = {Cohomology of Hopf Bimodules and Cup-product},
author = {Rachel Taillefer},
journal= {arXiv preprint arXiv:math/0005019},
year = {2009}
}
Comments
19pages, submitted to "Algebras and Representation Theory"