Keller admissible triples and Duflo theorem

Meeting Details

Abstract: The Hochschild cohomology of (associative) algebras can be generalized to dg algebras in two different ways. While the first kind of Hochschild cohomology of dg algebras admits a natural description in terms of a derived category of dg modules and is therefore preserved by quasi-isomorphisms of dg modules, the second kind of Hochschild cohomology is not. B. Keller proved that certain triples, which can be understood as a sort of Morita equivalences’ of dg algebras, induce isomorphisms of Hochschild cohomology of the first kind. In this talk, we will define another class of triples, which we call Keller admissible triples,’ that induce isomorphisms of Hochschild cohomology of the second kind. As an application, given a Lie algebra, we construct a Keller admissible triple and obtain an alternative proof of Duflo's theorem. This is a joint work with Hsuan-Yi Liao.