Clusters and seeds in acyclic cluster algebras

Details Clusters and seeds in acyclic cluster algebras Clusters and seeds in acyclic cluster algebras

2005-10-17

arxiv.org/abs/math/0510359v3

Mathematics

Representation Theory

12 pages, version3: added an appendix coauthored in addition by P. Caldero and B. Keller

Scientific paper

We show that for cluster algebras associated with finite quivers without oriented cycles (with no coefficients), a seed is determined by its cluster, as conjectured by Fomin and Zelevinsky.We also obtain an interpretation of the monomial in the denominator of a non-polynomial cluster variable in terms of the composition factors of an indecomposable exceptional module over an associated hereditary algebra.

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