Cluster algebras and symmetric matrices
arXiv:1201.4270
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.
9 pages; final version to appear in Proc. Amer. Math. Soc