2012/03/01 by Serge Bouc, Bouc, Serge, Radu Stancu +3
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras #math.GR
paper · pdf · doi:10.48550/arxiv.1203.0195
arxiv created 2012/03/01 · openalex publication_date 2012/03/01 · arxiv updated 2012/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.