G-structure on the cohomology of Hopf algebras

Farinati, Marco; Solotar, Andrea

doi:10.1090/S0002-9939-04-07274-0

G-structure on the cohomology of Hopf algebras
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by Marco A. Farinati and Andrea L. Solotar PDF

Proc. Amer. Math. Soc. 132 (2004), 2859-2865 Request permission

Abstract:

We prove that $\mathrm {Ext} ^{\bullet }_A(k,k)$ 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 imply the existence of a Gerstenhaber bracket on $H^{\bullet }_{GS}(H,H)$. This fact was conjectured by R. Taillefer. The method consists of identifying $H^{\bullet }_{GS}(H,H)\cong {\mathrm {Ext}}^{\bullet }_A(k,k)$ as a Gerstenhaber subalgebra of $H^{\bullet }(A,A)$ (the Hochschild cohomology of $A$).

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