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arXiv · 1901.03224

The Batalin-Vilkovisky structure on the Tate-Hochschild cohomology ring of a group algebra

Yuming Liu·Zhengfang Wang·Guodong Zhou
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Abstract

We determine the Batalin-Vilkovisky structure on the Tate-Hochschild cohomology of the group algebra $kG$ of a finite group $G$ in terms of the additive decomposition. In particular, we show that the Tate cohomology of $G$ is a Batalin-Vilkovisky subalgebra of the Tate-Hochschild cohomology of the group algebra $kG$, and that the Tate cochain complex of $G$ is a cyclic $A_{\infty}$-subalgebra of the Tate-Hochschild cochain complex of $kG$.

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Yuming Liu, Zhengfang Wang, Guodong Zhou. 2019-01-10. The Batalin-Vilkovisky structure on the Tate-Hochschild cohomology ring of a group algebra. https://arxiv.org/abs/1901.03224

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