Realising higher cluster categories of Dynkin type as stable module categories

Abstract

We show that the stable module categories of certain selfinjective algebras of finite representation type having tree class A_n, D_n, E_6, E_7 or E_8 are triangulated equivalent to u-cluster categories of the corresponding Dynkin type. The proof relies on the 'Morita' theorem for u-cluster categories by Keller and Reiten, along with the recent computation of Calabi-Yau dimensions of stable module categories by Dugas.

26 pages. This paper supersedes withdrawn preprints math.RT/0610728 and math.RT/0612451 which based the computation of Calabi-Yau dimensions on an erroneous result. The problem is circumvented here by using a recent paper of Alex Dugas