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arXiv · 1902.06245

The center of a Green biset functor

Serge Bouc·Nadia Romero
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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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Serge Bouc, Nadia Romero. 2019-02-17. The center of a Green biset functor. https://doi.org/10.2140/pjm.2019.303.459

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