A GEOMETRIC INTERPRETATION OF THE TRIANGULATED STRUCTURE OF m-CLUSTER CATEGORIES

摘要

The aim of this note is to answer several open problems arising from the geometric description of the m-cluster categories of type A_n and their realization in terms of the mth power of a translation quiver. In particular, we give a geometric interpretation of the triangulated structure of m-cluster categories. Furthermore, we characterize all the connected components arising from a cluster category when taking the mth power of its Auslander-Reiten (AR) quiver.