G-structure on the cohomology of Hopf algebras

We prove that Ext(A)(circle)(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 imply the existence of a Gerstenhaber bracket on H-GS(circle)(H, H). This fact was conjectured by R. Taillefer. The method consists of identifying H-GS(circle)(H, H) congruent to Ext(A)(circle)(k, k) as a Gerstenhaber subalgebra of H-circle(A, A) (the Hochschild cohomology of A).