REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Let A be any finite dimensional Hopf algebra over a field k. The aim of this talk is to extend a known relation of the cohomology and Hochschild cohomology of A to negative degrees. In particular, we prove that the Tate cohomology of A is an algebra direct summand of its Tate-Hochschild cohomology. If time permits, we will look at a computational example for the Sweedler algebra, and an application to finite group algebras. As this is an introductory talk, necessary background will be given.