English

The center of a Green biset functor

Group Theory 2022-01-06 v2 Category Theory Rings and Algebras Representation Theory

Abstract

For a Green biset functor AA, we define the commutant and the center of AA and we study some of their properties and their relationship. This leads in particular to the main application of these constructions: the possibility of splitting the category of AA-modules as a direct product of smaller abelian categories. We give explicit examples of such decompositions for some classical shifted representation functors. These constructions are inspired by similar ones for Mackey functors for a fixed finite group.

Keywords

Cite

@article{arxiv.1902.06245,
  title  = {The center of a Green biset functor},
  author = {Serge Bouc and Nadia Romero},
  journal= {arXiv preprint arXiv:1902.06245},
  year   = {2022}
}