Witt–Burnside ring and Burnside ring over a special λ-ring
نویسندگان
چکیده
منابع مشابه
A Note on the Λ-structure on the Burnside Ring
Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λ}n∈N. However, a priori λn(S), where S is a G-set, can only be computed recursively, by first computing λ1(S), . . . , λn−1(S). In this paper we establish an explicit formula, expressing λn(S) as a linear combination of classes of G-sets.
متن کاملA Note on the Λ-structure on the Burnside Ring
Let G be a finite group and let S be a G-set. The Burnside ring of G has a natural structure of a λ-ring, {λn}n∈N. However, a priori λ (S) can only be computed recursively, by first computing λ(S), . . . , λ(S). In this paper we establish an explicit formula, expressing λ(S) as a linear combination of classes of G-sets.
متن کاملThe 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 کاملThe extended Burnside ring and module categories
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...
متن کاملSimple biset functors and double Burnside ring
Let G be a finite group and let k be a field. Our purpose is to investigate the simple modules for the double Burnside ring kB(G,G). It turns out that they are evaluations at G of simple biset functors. For a fixed finite group H, we introduce a suitable bilinear form on kB(G,H) and we prove that the quotient of kB(−, H) by the radical of the bilinear form is a semi-simple functor. This allows ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2012
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2012.01.020