Orthogonal units of the bifree double Burnside ring
نویسندگان
چکیده
منابع مشابه
Simple 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 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 کاملThe functor of units of Burnside rings for p-groups
In this paper, I describe the structure of the biset functor B sending a p-group P to the group of units of its Burnside ring B(P ). In particular, I show that B is a rational biset functor. It follows that if P is a p-group, the structure of B(P ) can be read from a genetic basis of P : the group B(P ) is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational...
متن کاملThe Generalized Burnside Ring and the K–theory of a Ring with Roots of Unity
Determining the algebraic K-theory of rings of integers in number fields has been the goal of much research. In [10] D. Quillen showed that the Hurewicz map h : Q0(S ) → BGL(Z) (see 1.1 for the notation) induces an interesting map on homotopy groups from the stable homotopy groups of spheres to the algebraic K-theory of the ring Z of rational integers. Quillen observed that if ` is an odd prime...
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 Pure and Applied Algebra
سال: 2015
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2014.04.008