The center of a Green biset functor

Serge Bouc and Nadia Romero

Vol. 303 (2019), No. 2, 459–490

DOI: 10.2140/pjm.2019.303.459

Abstract

For a Green biset functor $A$, we define the commutant and the center of $A$ 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 $A$-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

biset functor, Green functor, functor category, center

Mathematical Subject Classification 2010

Primary: 16Y99, 18D10, 18D15, 20J15

Milestones

Received: 21 March 2019

Revised: 13 June 2019

Accepted: 21 June 2019

Published: 4 January 2020