Cluster algebras and symmetric matrices
Combinatorics
2013-05-13 v5 Representation Theory
Abstract
In this paper, we show that, for skew-symmetric cluster algebras, the c-vectors of any seed with respect to an acyclic initial seed define a quasi-Cartan companion of the corresponding exchange matrix. As an application, we show that any cluster tilted quiver has an admissible cut of edges.
Cite
@article{arxiv.1201.4270,
title = {Cluster algebras and symmetric matrices},
author = {Ahmet Seven},
journal= {arXiv preprint arXiv:1201.4270},
year = {2013}
}
Comments
9 pages; final version to appear in Proc. Amer. Math. Soc