CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES


Creative Commons License

Seven A. İ.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.147, pp.2809-2814, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 147
  • Publication Date: 2019
  • Doi Number: 10.1090/proc/14459
  • Title of Journal : PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Page Numbers: pp.2809-2814

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.