On the graded center of the stable category of a finite p-group

2008/11/27 by Markus Linckelmann, Linckelmann, Markus, Radu Stancu +1
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #math.CT #math.RT

paper · pdf · doi:10.48550/arxiv.0811.4626

14 pages

arxiv created 2008/11/27 · arxiv updated 2009/12/01

Abstract

We show that for any finite p-group P of rank at least 2 and any algebraically closed field k of characteristic p the graded center Z^*(\modbar(kP)) of the stable module category of finite-dimensional kP-modules has infinite dimension in each odd degree, and if p=2 also in each even degree. In particular, this provides examples of symmetric algebras A for which Z⁰(\modbar(A)) is not finite-dimensional, answering a question raised in [10]

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