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arXiv · 2010.07505

Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies

Tekin Karadağ
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Abstract

We calculate the Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies of the Taft algebra $T_p$ for any integer $p>2$ which is a nonquasi-triangular Hopf algebra. We show that the bracket is indeed zero on Hopf algebra cohomology of $T_p$, as in all known quasi-triangular Hopf algebras. This example is the first known bracket computation for a nonquasi-triangular algebra. Also, we find a general formula for the bracket on Hopf algebra cohomology of any Hopf algebra with bijective antipode on the bar resolution that is reminiscent of Gerstenhaber's original formula for Hochschild cohomology.

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BibTeXRIS

Tekin Karadağ. 2020-10-15. Gerstenhaber bracket on Hopf algebra and Hochschild cohomologies. https://arxiv.org/abs/2010.07505

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