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

2019/01/10 by Yuming Liu, Liu, Yuming, Zhengfang Wang +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1901.03224

openalex publication_date 2019/01/10 · openalex created_date 2019/02/21 · openalex updated_date 2026/08/01

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_∞-subalgebra of the Tate-Hochschild cochain complex of kG.

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