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The Batalin-Vilkovisky structure on the Tate-Hochschild cohomology ring of a group algebra (1901.03224v1)
Published 10 Jan 2019 in math.GR, math.KT, and math.RT
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 $kG$.