Cluster combinatorics of d-cluster categories

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dc.creatorZhou, Yu
dc.creatorZhu, Bin
dc.date2007-12-10
dc.date2009-02-14
dc.date.accessioned2026-07-07T12:41:04Z
dc.date.available2026-07-07T12:41:04Z
dc.descriptionWe study the cluster combinatorics of $d-$cluster tilting objects in $d-$cluster categories. By using mutations of maximal rigid objects in $d-$cluster categories which are defined similarly for $d-$cluster tilting objects, we prove the equivalences between $d-$cluster tilting objects, maximal rigid objects and complete rigid objects. Using the chain of $d+1$ triangles of $d-$cluster tilting objects in [IY], we prove that any almost complete $d-$cluster tilting object has exactly $d+1$ complements, compute the extension groups between these complements, and study the middle terms of these $d+1$ triangles. All results are the extensions of corresponding results on cluster tilting objects in cluster categories established in [BMRRT] to $d-$cluster categories. They are applied to the Fomin-Reading's generalized cluster complexes of finite root systems defined and studied in [FR2] [Th] [BaM1-2], and to that of infinite root systems [Zh3].
dc.descriptioncorreted many typos according to the referee's comments, final version to appear in J. Algebra
dc.identifierhttps://arxiv.org/abs/0712.1381
dc.identifierhttp://arxiv.org/abs/0712.1381
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/219647
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject16G20, 16G70, 05A15,
dc.titleCluster combinatorics of d-cluster categories
dc.typetext

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