The relative Heller operator and relative cohomology for the Klein 4-group

2021/07/02 by Elmer, Jonatan · 1 citation
#20C20 #20J06 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2107.00991

Abstract

Let G be the Klein Four-group and let k be an arbitrary field of characteristic 2. A classification of indecomposable kG-modules is known. We calculate the relative cohomology groups H_\chiⁱ(G,N) for every indecomposable kG-module N, where \chi is the set of proper subgroups in G. This extends work of Pamuk and Yalcin to cohomology with non-trivial coefficients. We also show that all cup products in strictly positive degree in H_\chi^*(G,k) are trivial.

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