CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES


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Seven A. İ.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.147, ss.2809-2814, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 147
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1090/proc/14459
  • Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Sayfa Sayıları: ss.2809-2814

Özet

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.