G-Structure on the cohomology of Hopf algebras

Abstract

We prove that Ext^*_A(k,k) is a Gerstenhaber algebra, where A is a Hopf algebra. In case A=D(H) is the Drinfeld double of a finite dimensional Hopf algebra H, our results implies the existence of a Gerstenhaber bracket on H^*_{GS}(H,H). This fact was conjectured by R. Taillefer in math.KT0207154. The method consists in identifying Ext^*_A(k,k) as a Gerstenhaber subalgebra of H^*(A,A) (the Hochschild cohomology of A).