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International Mathematics Research Notices (2007) Vol. 2007 : article ID rnm011, 19 pages, doi:10.1093/imrn/rnm011 published on May 24, 2007
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Copyright © The Author 2007. Published by Oxford University Press.

A Geometric Description of the m-cluster Categories of Type Dn

Karin Baur1, and Robert J. Marsh2

1 Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, England, UK
2 Department of PureMathematics, University of Leeds, Leeds LS2 9JT, England, UK

Correspondence: Correspondence to be sent to: Karin Baur, Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, England, UK. e-mail: k.baur{at}mcs.le.ac.uk

We show that the m-cluster category of type Dn is equivalent to a certain geometrically-defined category of arcs in a punctured regular nm – m + 1-gon. This generalizes a result of Schiffler for m = 1. We use the notion of the mth power of a translation quiver to realize the m-cluster category in terms of the cluster category.

Communicated by Andrei Zelevinsky


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