Quivers with relations and cluster tilted algebras

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dc.creatorCaldero, Philippe
dc.creatorChapoton, Frederic
dc.creatorSchiffler, Ralf
dc.date2004-11-10
dc.date.accessioned2026-07-07T06:24:13Z
dc.date.available2026-07-07T06:24:13Z
dc.descriptionCluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. To a cluster algebra of simply laced Dynkin type one can associate the cluster category. Any cluster of the cluster algebra corresponds to a tilting object in the cluster category. The cluster tilted algebra is the algebra of endomorphisms of that tilting object. Viewing the cluster tilted algebra as a path algebra of a quiver with relations, we prove in this paper that the quiver of the cluster tilted algebra is equal to the cluster diagram. We study also the relations. As an application of these results, we answer several conjectures on the connection between cluster algebras and quiver representations.
dc.description19 pages, 3 figures
dc.identifierhttps://arxiv.org/abs/math/0411238
dc.identifierhttp://arxiv.org/abs/math/0411238
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96466
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16G20, 16G70
dc.titleQuivers with relations and cluster tilted algebras
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