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arXiv · 2107.00991

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

Jonatan Elmer
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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 $H_\{chi}^i(G,N)$ 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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Jonatan Elmer. 2021-07-02. The relative Heller operator and relative cohomology for the Klein 4-group. https://arxiv.org/abs/2107.00991

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