Marsh, RJ and Palu, Y (2013) Coloured quivers for rigid objects and partial triangulations: The unpunctured case. Proceedings of the London Mathematical Society. 1 - 29. ISSN 0024-6115
Abstract
We associate a coloured quiver to a rigid object in a Hom-finite 2-Calabi–Yau triangulated category and to a partial triangulation on a marked (unpunctured) Riemann surface. We show that, in the case where the category is the generalised cluster category associated to a surface, the coloured quivers coincide. We also show that compatible notions of mutation can be defined and give an explicit description in the case of a disk. We show further that Iyama-Yoshino reduction can be interpreted as cutting along an arc in the surface.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | (c) 2013, London Mathematical Society. This is an author produced version of a paper published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy |
Keywords: | Representation theory; category theory; geometric topology |
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: | 21 Nov 2013 10:19 |
Last Modified: | 28 Mar 2018 18:46 |
Published Version: | http://plms.oxfordjournals.org/cgi/reprint/pdt032 |
Status: | Published |
Publisher: | London Mathematical Society |
Refereed: | Yes |
Identification Number: | 10.1112/plms/pdt032 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:77023 |