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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 Alperin's 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 Alperin's weight conjecture for finite groups and for finite categories are in fact equivalent. © 2013 Elsevier Inc.
|Uncontrolled Keywords:||Category algebra; Weight conjecture|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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