authors:

Markus Linckelmann and Radu Stancu


title:

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


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 $Z^0(\modbar(A))$ is not finite-dimensional,
answering a question raised in \cite{Li2}.


status:

submited to J of Pure and Applied Algebra