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

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

2008-11-27

arxiv.org/abs/0811.4626v1

Mathematics

Representation Theory

14 pages

Scientific paper

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 $Z^0(\modbar(A))$ is not finite-dimensional, answering a question raised in [10]

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