2-Calabi-Yau categories associated with Coxeter group elements

Osamu Iyama

We construct a class of 2-Calabi-Yau triangulated categories related to preprojective algebras associated with elements in the Coxeter group. For these 2-Calabi-Yau categories we construct cluster tilting objects associated with each reduced expression. The endomorphism algebra is presented by a quiver with potential, which is described in terms of the reduced expression. This class of 2-Calabi-Yau categories contains the cluster categories and the stable categories of preprojective algebras of Dynkin graphs as special cases.