CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.147, pp.2809-2814, 2019 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 147
- Publication Date: 2019
- Doi Number: 10.1090/proc/14459
- Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2809-2814
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
Abstract
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.