Quivers with relations arising from clusters (A_n case)

Details Quivers with relations arising from clusters (A_n case) Quivers with relations arising from clusters (A_n case)

2004-01-23

arxiv.org/abs/math/0401316v1

Mathematics

Representation Theory

18 pages, 6 figures

Scientific paper

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.

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