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

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arxiv 1901.03224 v1 pith:3JDHRU5X submitted 2019-01-10 math.GR math.KTmath.RT

Yuming Liu , Zhengfang Wang , Guodong Zhou This is my paper · ORCID
classification math.GRmath.KTmath.RT
keywords cohomologygrouptate-hochschildalgebrabatalin-vilkoviskycochaincomplexstructure
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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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  1. Monoidal structures arising from $B_\infty$-algebras with applications to Hopf algebras

    math.RT 2026-08 conditional novelty 8.0 of 10

    A B-infinity structure on an algebra gives a monoidal tensor product on the derived category of right modules, and for Hopf algebras this produces an algebraic proof of the Benson-Krause monoidal equivalence.

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