CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, cilt.147, ss.2809-2814, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 147
- Basım Tarihi: 2019
- Doi Numarası: 10.1090/proc/14459
- Dergi Adı: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.2809-2814
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
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.