A geometric description of the m-cluster categories of type D_n

Details A geometric description of the m-cluster categories of type D_n A geometric description of the m-cluster categories of type D_n

2006-10-17

arxiv.org/abs/math/0610512v1

International Mathematical Research Notices (2007) Vol. 2007

Mathematics

Representation Theory

14 pages, 11 figures

Scientific paper

10.1093/imrn/rnm011

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.

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