Colloque 2013 du GDR 2875, Topologie Algébrique et Applications

16-18 October 2013
Université d'Angers
Europe/Paris timezone

Simple biset functors and the double Burnside ring

16 Oct 2013, 10:00
45m
Amphi L005 (bâtiment L) (Université d'Angers)

Amphi L005 (bâtiment L)

Université d'Angers

Université d'Angers, 2 Boulevard Lavoisier, 49045 Angers cedex 01
Exposé de recherche sur invitation Topologie algébrique et applications

Speaker

Dr Radu Stancu (LAMFA, Université de Picardie)

Description

This is a joint work with Serge Bouc and Jacques Thévenaz. Let G be a finite group and k be a field. The purpose of this talk is to investigate the simple modules for the double Burnside ring kB(G;G). It turns out that these modules 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 prove that the quotient of the functor kB(-;H) by the radical of the bilinear form is semi-simple. This allows for a description of the evaluation of simple functors, hence of simple modules for the double Burnside ring. The evaluation of a simple biset functor at a finite group G may be zero. We give examples where this happens, as well as where this does not occur. Under some restrictive conditions on G we can give a closed formula for such an evaluation.
Mots Clés / Keywords double Burnside ring, simple biset fuctors

Primary author

Dr Radu Stancu (LAMFA, Université de Picardie)

Presentation Materials

 Transparents