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arXiv · 1203.0195

Simple biset functors and double Burnside rings

Serge Bouc·Radu Stancu·Jacques Thévenaz
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Abstract

Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are evaluations at G of simple biset functors. For a fixed finite group H, we introduce a suitable bilinear form on kB(G,H) and we prove that the quotient of kB(-,H) by the radical of the bilinear form is a semi-simple functor. This allows for a description of the evaluation of simple functors, hence of simple modules for the double Burnside ring.

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Serge Bouc, Radu Stancu, Jacques Thévenaz. 2012-03-01. Simple biset functors and double Burnside rings. https://arxiv.org/abs/1203.0195

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