  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).
