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G-Structure on the cohomology of Hopf algebras

M. Farinati·A. Solotar
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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).

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M. Farinati, A. Solotar. 2002-07-25. G-Structure on the cohomology of Hopf algebras. https://arxiv.org/abs/math/0207243

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