Secondary multiplication in Tate cohomology of certain p-groups

Details Secondary multiplication in Tate cohomology of certain p-groups Secondary multiplication in Tate cohomology of certain p-groups

2008-03-03

arxiv.org/abs/0803.0252v1

Mathematics

Algebraic Topology

35 pages

Scientific paper

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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