Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Cluster algebras and symmetrizable matrices


Author: Ahmet I. Seven
Journal: Proc. Amer. Math. Soc. 147 (2019), 2809-2814
MSC (2010): Primary 05E15; Secondary 13F60
DOI: https://doi.org/10.1090/proc/14459
Published electronically: March 15, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In the structure theory of cluster algebras, principal coefficients are parametrized by a family of integer vectors, called $ \mathbf {c}$-vectors. Each $ \mathbf {c}$-vector with respect to an acyclic initial seed is a real root of the corresponding root system, and the $ \mathbf {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 $ \mathbf {c}$-vectors define an admissible cut of edges in the associated diagrams.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 05E15, 13F60

Retrieve articles in all journals with MSC (2010): 05E15, 13F60


Additional Information

Ahmet I. Seven
Affiliation: Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey
Email: aseven@metu.edu.tr

DOI: https://doi.org/10.1090/proc/14459
Received by editor(s): April 10, 2018
Received by editor(s) in revised form: October 2, 2018
Published electronically: March 15, 2019
Additional Notes: The author’s research was supported in part by the Scientific and Technological Research Council of Turkey (TUBITAK) grant #116F205.
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society