Cluster algebras of finite type via Coxeter elements and principal minors

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dc.creatorYang, Shih-Wei
dc.creatorZelevinsky, Andrei
dc.date2008-04-21
dc.date2008-05-19
dc.date.accessioned2026-07-07T09:39:19Z
dc.date.available2026-07-07T09:39:19Z
dc.descriptionWe give a uniform geometric realization for the cluster algebra of an arbitrary finite type with principal coefficients at an arbitrary acyclic seed. This algebra is realized as the coordinate ring of a certain reduced double Bruhat cell in the simply connected semisimple algebraic group of the same Cartan-Killing type. In this realization, the cluster variables appear as certain (generalized) principal minors.
dc.description38 pages, 2 figures; v2: minor editorial changes, to appear in Transformation Groups
dc.identifierhttps://arxiv.org/abs/0804.3303
dc.identifierhttp://arxiv.org/abs/0804.3303
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161129
dc.subjectRings and Algebras
dc.subjectRepresentation Theory
dc.subject16S99 (Primary); 17B20, 22E46 (Secondary)
dc.titleCluster algebras of finite type via Coxeter elements and principal minors
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