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Article Dans Une Revue Trans. Amer. Math. Soc. Année : 2006

Quivers with relations arising from clusters (A_n case)

Résumé

Cluster 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.

Dates et versions

hal-00120665 , version 1 (16-12-2006)

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Philippe Caldero, Frédéric Chapoton, Ralf Schiffler. Quivers with relations arising from clusters (A_n case). Trans. Amer. Math. Soc., 2006, 358 numéro 3, pp.1347-1364. ⟨hal-00120665⟩
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