Linckelmann, M. (2013). A version of alperin's weight conjecture for finite category algebras. Journal of Algebra, 398, pp. 386395. doi: 10.1016/j.jalgebra.2013.02.010

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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 psubgroups 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 kCmodules 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.
Item Type:  Article 

Uncontrolled Keywords:  Category algebra; Weight conjecture 
Subjects:  Q Science > QA Mathematics 
Divisions:  School of Engineering & Mathematical Sciences > Department of Mathematical Science 
URI:  http://openaccess.city.ac.uk/id/eprint/7346 
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