On the T∘-slices of a finite group

Tounkara, Ibrahima

doi:10.1016/j.crma.2018.03.001

Comptes Rendus. Mathématique

2018

DOI: 10.1016/j.crma.2018.03.001

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On the T∘-slices of a finite group

Ibrahima Tounkara

Abstract: Algebra/Group theory On the T • -slices of a finite group ✩ Sur les T • -tranches d'un groupe fini

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2019

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The center of a Green biset functor

Bouc

Romero

2019

Pacific J. Math.

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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. We fix a non-empty class D of finite groups closed under subquotients and cartesian products, and a set D of representatives of isomorphism classes of groups in D. We denote by RD the full subcategory of RC consisting of groups in D, so in particular RD is a replete subcategory of RC, in the sense of [2], Definition 4.1.7. The category of biset functors, i.e. the category of R-linear functors from RC to the category R-Mod of all R-modules, will be denoted by Fun R . The category Fun D,R of D-biset functors is the category of R-linear functors from RD to R-Mod.

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The center of a Green biset functor

Bouc

Romero

2019

Pacific J. Math.

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On the T∘-slices of a finite group

Abstract: Algebra/Group theory On the T • -slices of a finite group ✩ Sur les T • -tranches d'un groupe fini

Cited by 1 publication

References 8 publications

The center of a Green biset functor

The center of a Green biset functor

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