Hochschild homology of Hopf algebras and free Yetter-Drinfeld modules

Julien Bichon (U Clermont-Ferrand)

Wednesday 13th March, 2013 16:00-17:00 204


We explain how one can relate the Hochschild (co)homologies of Hopf algebras having equivalent tensor categories of comodules, in case the trivial module over one of the Hopf algebras admits a resolution by free Yetter-Drinfeld modules. This general procedure is applied to the quantum group of a bilinear form, for which generalizations of results by Collins, Hartel and Thom in the orthogonal case are obtained. It also will be shown that the Gerstenhaber-Schack cohomology of a cosemisimple Hopf algebra completely determines its Hochschild cohomology.

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