Secondary multiplication in Tate cohomology of certain p-groups

2008/03/03 by Martin Langer, Langer, Martin
Mathematics · #20J06 (Primary) #55S35 (Secondary) #Advanced Algebra and Geometry #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0803.0252

openalex publication_date 2008/03/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k be a field and let G be a finite group. By a theorem of D.Benson, H.Krause and S.Schwede, there is a canonical element in the Hochschild cohomology of the Tate cohomology HH^3,-1 H*G with the following property: Given any graded H*G-module X, the image of the canonical element in Ext^3,-1(X,X) is zero if and only if X is isomorphic to a direct summand of H*(G,M) for some kG-module M. We investigate this canonical element in certain special cases, namely that of (finite) abelian p-groups and the quaternion group. In case of non-triviality of the canonical element, we also give examples of non-realizable modules X.

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