Fibered biset functors
نویسندگان
چکیده
منابع مشابه
Rational p-biset functors
In this paper, I give several characterizations of rational biset functors over p-groups, which are independent of the knowledge of genetic bases for p-groups. I also introduce a construction of new biset functors from known ones, which is similar to the Yoneda construction for representable functors, and to the Dress construction for Mackey functors, and I show that this construction preserves...
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Rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism. The rhetorical p-biset functors almost coincide with the rational p-biset functors. We show that, over a field with characteristic zero, the rhetorical biset functors are semisimple and, furthermore, they admit a character theory involving primitive characters of automor...
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Let p be an odd prime number. In this paper, we show that the genome Γ(P ) of a finite p-group P , defined as the direct product of the genotypes of all rational irreducible representations of P , can be recovered from the first group of K-theory K1(QP ). It follows that the assignment P 7→ Γ(P ) is a p-biset functor. We give an explicit formula for the action of bisets on Γ, in terms of genera...
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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 ...
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The idea of a moduli space is that its points correspond to a geometric object of interest. The underlying set of the space is thus determined, but not its geometric structure. In most cases, one can describe a geometric structure in an ad hoc manner, but it is not immediately obvious how to rigorously formulate the idea that the resulting object is “the” moduli space for the problem. This is t...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2018
ISSN: 0001-8708
DOI: 10.1016/j.aim.2018.09.034