Clusters and seeds in acyclic cluster algebras
Representation Theory
2020-12-21 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0510359,
title = {Clusters and seeds in acyclic cluster algebras},
author = {Aslak Bakke Buan and Bethany Marsh and Idun Reiten and Gordana Todorov},
journal= {arXiv preprint arXiv:math/0510359},
year = {2020}
}
Comments
12 pages, version3: added an appendix coauthored in addition by P. Caldero and B. Keller