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The slice Burnside ring and the section Burnside ring of a finite group

Part of: Grothendieck groups and $K_0$ Categories and geometry

Published online by Cambridge University Press:  22 March 2012

Serge Bouc
Serge Bouc*
Affiliation:
CNRS-LAMFA, Université de Picardie, 33 rue St Leu, 80039, Amiens cedex 1, France (email: serge.bouc@u-picardie.fr)
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Abstract

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This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets and of Galois morphisms of G-sets, respectively. The well-known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are extended to these rings. It is also shown that these two rings have a natural Green biset functor structure. The functorial structure of unit groups of these rings is also discussed.

Keywords

Burnside ringGreen biset functorslicesectionunit group

MSC classification

Secondary: 19A22: Frobenius induction, Burnside and representation rings 18F30: Grothendieck groups
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 868 - 906
Copyright
Copyright © Foundation Compositio Mathematica 2012

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