CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES

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2019-07-01

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Seven, Ahmet İrfan

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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.

Subject Keywords

Applied Mathematics, General Mathematics

URI

https://hdl.handle.net/11511/36450

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

DOI

https://doi.org/10.1090/proc/14459

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Department of Mathematics, Article

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Citation Formats

A. İ. Seven, “CLUSTER ALGEBRAS AND SYMMETRIZABLE MATRICES,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 2809–2814, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36450.