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Abstract
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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.
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Keywords
biset functor, Green functor, functor category, center
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Mathematical Subject Classification 2010
Primary: 16Y99, 18D10, 18D15, 20J15
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Milestones
Received: 21 March 2019
Revised: 13 June 2019
Accepted: 21 June 2019
Published: 4 January 2020
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