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

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

2011-01-17

arxiv.org/abs/1101.3138v1

Mathematics

Group Theory

Scientific paper

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 structure of Green biset functor. The functorial structure of unit groups of these rings is also discussed.

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