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Quivers with relations arising from clusters (A_n case)

By Philippe Caldero, Frederic Chapoton and Ralf Schiffler

Abstract

18 pages, 6 figuresCluster algebras were introduced by S. Fomin and A. Zelevinsky in connection with dual canonical bases. Let U be a cluster algebra of type A_n. We associate to each cluster C of U an abelian category Cat_C such that the indecomposable objects of Cat_C are in natural correspondence with the cluster variables of U which are not in C. We give an algebraic realization and a geometric realization of Cat_C. Then, we generalize the ``denominator Theorem'' of Fomin and Zelevinsky to any cluster

Topics: [MATH.MATH-RT] Mathematics [math]/Representation Theory [math.RT], [MATH.MATH-RA] Mathematics [math]/Rings and Algebras [math.RA]
Publisher: HAL CCSD
Year: 2006
OAI identifier: oai:HAL:hal-00120665v1
Provided by: Hal-Diderot
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