Article ID Journal Published Year Pages File Type
6414817 Journal of Algebra 2014 10 Pages PDF
Abstract

Let p be a prime and k an algebraically closed field of characteristic p. We construct a functor C→OC on the category of finite categories with the property that if G=C is a finite group, then OC is the orbit category of p-subgroups of G. This leads to an extension of Alperinʼs weight conjecture to any finite category C, stating that the number of isomorphism classes of simple kC-modules should be equal to that of the weight algebra W(kOC) of OC. We show that the versions of Alperinʼs weight conjecture for finite groups and for finite categories are in fact equivalent.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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