CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES

Download
2019-07-01
In the structure theory of cluster algebras, principal coefficients are parametrized by a family of integer vectors, called c-vectors. Each c-vector with respect to an acyclic initial seed is a real root of the corresponding root system, and the c-vectors associated with any seed defines a symmetrizable quasi-Cartan companion for the corresponding exchange matrix. We establish basic combinatorial properties of these companions. In particular, we show that c-vectors define an admissible cut of edges in the associated diagrams.

Citation Formats
A. İ. Seven, “CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 147, pp. 2809–2814, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36450.