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arXiv · 1405.5155

BV-differential on Hochschild cohomology of Frobenius algebras

Yury Volkov
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Abstract

For a finite-dimensional Frobenius $k$-algebra $R$ with the Nakayama automorphism $ν$ we define an algebra ${\rm HH}^*(R)^{ν\uparrow}$. If the order of $ν$ is not divisible by the characteristic of $k$, this algebra is isomorphic to the Hochschild cohomology algebra of $R$.. We prove that this algebra is a BV-algebra. We use this fact to calculate the Gerstenhaber algebra structure and BV-structure on the Hochschild cohomology algebras of a family of self-injective algebras of tree type $D_n$.

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Yury Volkov. 2014-05-20. BV-differential on Hochschild cohomology of Frobenius algebras. https://arxiv.org/abs/1405.5155

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