Vol. 303, No. 2, 2019

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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.

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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
Authors
Serge Bouc
CNRS-LAMFA
Université de Picardie
Amiens
France
Nadia Romero
Departamento de Matemáticas
Universidad de Guanajuato
Guanajuato
Mexico