Abstract
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.
ACKNOWLEDGMENTS
I would like to thank Prof. K. Baur for introducing me to such an interesting field, for the inspiring discussions we had and for her time in reading my drafts.
Notes
Communicated by Q. Wu.