• Corpus ID: 119638953

Simple biset functors and double Burnside rings

@article{Bouc2012SimpleBF,
  title={Simple biset functors and double Burnside rings},
  author={Serge Bouc and Radu Stancu and Jacques Th'evenaz},
  journal={arXiv: Group Theory},
  year={2012}
}
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… 
3 Citations
Ghost Algebras of Double Burnside Algebras via Schur Functors
For a finite group G, we introduce a multiplication on the Q-vector space with basis SG×G, the set of subgroups of G × G. The resulting Q-algebra à can be considered as a ghost algebra for the double

References

SHOWING 1-10 OF 14 REFERENCES
Gluing torsion endo‐permutation modules
Let k be a field of characteristic p, and let P be a finite p‐group, where p is an odd prime. In this paper, we consider the problem of gluing compatible families of endo‐permutation modules: being
The Dade group of a p-group
Let p be a prime number. This paper solves the question of the structure of the group D(P) of endo-permutation modules over an arbitrary finite p-group P, that was open after Dade’s original papers
Biset Functors for Finite Groups
Examples.- General properties.- -Sets and (, )-Bisets.- Biset Functors.- Simple Functors.- Biset functors on replete subcategories.- The Burnside Functor.- Endomorphism Algebras.- The Functor.-
Saturated fusion systems as idempotents in the double Burnside ring
We give a new characterization of saturated fusion systems on a p ‐group S in terms of idempotents in the p ‐local double Burnside ring of S that satisfy a Frobenius reciprocity relation.
Classifying spectra of saturated fusion systems
The assignment of classifying spectra to saturated fusion systems was suggested by Linckelmann and Webb and has been carried out by Broto, Levi and Oliver. A more rigid (but equivalent) construction
Foncteurs d'ensembles munis d'une double action
Resume SOMMAIRE 1.Introduction 2.Notations. Generalites. 3.Ensembles munis d'une double action. 3.1. Notations. 3.2. Formule de Mackey. 3.3. Decomposition d'un morphisme. 3.4. Sous-categories. 3.4.1.
...
1
2
...