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The center of a Green
biset functor
Serge Bouc and Nadia Romero |
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Vol. 303 (2019), No. 2, 459–490
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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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Authors |
| Serge Bouc | |
| CNRS-LAMFA Université de Picardie Amiens France |
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| Nadia Romero | |
| Departamento de Matemáticas Universidad de Guanajuato Guanajuato Mexico |
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