A geometric description of the m-cluster categories of type D_n
arXiv:math/0610512 · doi:10.1093/imrn/rnm011
Abstract
We show that the m-cluster category of type D_n is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm-m+1-gon. This generalises a result of Schiffler for m=1. We use the notion of the mth power of a translation quiver to realise the m-cluster category in terms of the cluster category.
14 pages, 11 figures