A geometric interpretation of the triangulated structure of m-cluster categories

Details A geometric interpretation of the triangulated structure of m-cluster categories A geometric interpretation of the triangulated structure of m-cluster categories

2011-07-06

arxiv.org/abs/1107.1041v1

Mathematics

Representation Theory

Scientific paper

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 $m$-th 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 $m$-th power of its Auslander-Reiten quiver.

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