A geometric description of $m$-cluster categories

Details A geometric description of $m$-cluster categories A geometric description of $m$-cluster categories

2006-07-06

arxiv.org/abs/math/0607151v1

Trans. Amer. Math. Soc. 360 (2008), 5789-5803

Mathematics

Representation Theory

14 pages, 5 figures

Scientific paper

We show that the $m$-cluster category of type $A_{n-1}$ is equivalent to a certain geometrically-defined category of diagonals of a regular $nm+2$-gon. This generalises a result of Caldero, Chapoton and Schiffler for $m=1$. The approach uses the theory of translation quivers and their corresponding mesh categories. We also introduce the notion of the $m$th power of a translation quiver and show how it can be used to realise the $m$-cluster category in terms of the cluster category.

Affiliated with

Also associated with

No associations

Rating

A geometric description of $m$-cluster categories does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A geometric description of $m$-cluster categories, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A geometric description of $m$-cluster categories will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-45491