Laurent expansions in cluster algebras via quiver representations
Representation Theory
2007-05-23 v4 Algebraic Geometry
Combinatorics
Abstract
We study Laurent expansions of cluster variables in a cluster algebra of rank 2 associated to a generalized Kronecker quiver. In the case of the ordinary Kronecker quiver, we obtain explicit expressions for Laurent expansions of the elements of the canonical basis for the corresponding cluster algebra.
Keywords
Cite
@article{arxiv.math/0604054,
title = {Laurent expansions in cluster algebras via quiver representations},
author = {Philippe Caldero and Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0604054},
year = {2007}
}
Comments
19 pages; v2: added Remark 5.7; v3: minor editorial changes, final version to appear in Moscow Math. Journal; v4: more minor editorial changes