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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer Berlin Heidelberg

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DOI

10.1007/PL00021204

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1432-1823

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Cluster categories of type mathbb A infty

Authors: Shiping Liu Charles Paquette
Publish Date: 2016/10/04
Volume: 286, Issue: 1-2, Pages: 197-222
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Abstract

We call a 2Calabi–Yau triangulated category a cluster category if its clustertilting subcategories form a cluster structure as defined in Buan et al Compos Math 1451035–1079 2009 In this paper we show that the canonical orbit category of the bounded derived category of finite dimensional representations of a quiver without infinite paths of type mathbb A infty or mathbb A infty infty is a cluster category Moreover for a cluster category of type mathbb A infty infty we give a geometrical description of its cluster structure in terms of triangulations of an infinite strip with marked points in the planeBoth authors were supported in part by the Natural Science and Engineering Research Council of Canada while the secondnamed author was also supported in part by the Atlantic Association for Research in the Mathematical Sciences They are grateful to the referee for drawing their attention to the references 11 13

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