#### Vol. 303, No. 2, 2019

 Recent Issues Vol. 306: 1  2 Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
The center of a Green biset functor

### Serge Bouc and Nadia Romero

Vol. 303 (2019), No. 2, 459–490
##### 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