On a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon

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dc.creatorHolm, Thorsten
dc.creatorJorgensen, Peter
dc.date2009-02-24
dc.date.accessioned2026-07-07T12:46:13Z
dc.date.available2026-07-07T12:46:13Z
dc.descriptionThis paper investigates a certain 2-Calabi-Yau triangulated category D whose Auslander-Reiten quiver is ZA_{\infty}. We show that the cluster tilting subcategories of D form a so-called cluster structure, and we classify these subcategories in terms of what one may call `triangulations of the infinity-gon'. This is reminiscent of the cluster category C of type A_n which is a 2-Calabi-Yau triangulated category whose Auslander-Reiten quiver is a quotient of ZA_n. The cluster tilting subcategories of C form a cluster structure and they are classified in terms of triangulations of the (n+3)-gon. The category D behaves like a `cluster category of type A_{\infty}'.
dc.description20 pages
dc.identifierhttps://arxiv.org/abs/0902.4125
dc.identifierhttp://arxiv.org/abs/0902.4125
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/221305
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject16E45, 16G20, 16G70
dc.titleOn a triangulated category which behaves like a cluster category of infinite Dynkin type, and the relation to triangulations of the infinity-gon
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