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 , we define the commutant and the center of 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 -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.
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}
}