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

Karin Baur·Bethany Marsh
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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.

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Karin Baur, Bethany Marsh. 2006-10-17. A geometric description of the m-cluster categories of type D_n. https://doi.org/10.1093/imrn%2Frnm011

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