2006/07/06 by Karin Baur, Bethany Marsh · 1 citation
Mathematics · #math.RT #math.RA #msc:16G20 #msc:16G70 #msc:18E30
published as Trans. Amer. Math. Soc. 360 (2008), 5789-5803 · 14 pages, 5 figures
arxiv created 2006/07/06 · arxiv updated 2020/12/21
We show that the m-cluster category of type An-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 mth power of a translation quiver and show how it can be used to realise the m-cluster category in terms of the cluster category.