Decomposition of the Witt–Burnside ring and Burnside ring of an abelian profinite group
نویسندگان
چکیده
منابع مشابه
The slice Burnside ring and the section Burnside ring of a finite group
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 ex...
متن کاملGeneralized Burnside-grothendieck Ring Functor and Aperiodic Ring Functor Associated with Profinite Groups
For every profinite group G, we construct two covariant functors ∆G and APG from the category of commutative rings with identity to itself, and show that indeed they are equivalent to the functor WG introduced in [A. Dress and C. Siebeneicher, The Burnside ring of profinite groups and the Witt vectors construction, Adv. Math. 70 (1988), 87-132]. We call ∆G the generalized Burnside-Grothendieck ...
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In this note we present an algorithm for the construction of the unit group of the Burnside ring Ω(G) of a finite group G from a list of representatives of the conjugacy classes of subgroups of G.
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2 In the hallway of the university Wittgenstein asked a colleague: " I've always wondered why for so long people thought that the sun revolved around the earth. " " Why? " said his surprised interlocutor, " well, I suppose it just looks that way. " " Hmm " , retorted Wittgenstein, " and what would it look like if the earth revolved around the sun? " This puzzled the interlocutor.
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In this note an ‘extended Burnside ring’ is defined, generated by classes of semisimple module categories over Rep(G) with quasifibre functors. Here G is a finite group and representations are taken over an algebraically closed field of characteristic 0. It is shown that this is equivalent to a ring generated by centrally extended G-sets and hence the name. Ring homomorphisms into the multiplic...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2009
ISSN: 0001-8708
DOI: 10.1016/j.aim.2009.05.004