Baur, K orcid.org/0000-0002-7665-476X and Marsh, RJ orcid.org/0000-0002-4268-8937 (2007) A geometric description of the m-cluster categories of type Dn. International Mathematics Research Notices, 2007. rnm011. ISSN 1073-7928
Abstract
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 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.
Metadata
Item Type: | Article |
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Authors/Creators: | |
Copyright, Publisher and Additional Information: | Copyright © The Author 2007. Published by Oxford University Press. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices, following peer review. The version of record is available online at: https://doi.org/10.1093/imrn/rnm011 |
Keywords: | cluster algebra; derived category; cluster category; m-cluster category; polygon dissection; m-divisible; simplicial complex; mesh category; Auslander-Reiten quiver; triangulated category; type Dn |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 03 Sep 2019 14:26 |
Last Modified: | 03 Sep 2019 14:26 |
Status: | Published |
Publisher: | Oxford University Press |
Identification Number: | 10.1093/imrn/rnm011 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:149688 |