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CLUSTER ALGEBRAS AND SYMMETRIC MATRICES
Date
2015-02-01
Author
Seven, Ahmet İrfan
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In the structural theory of cluster algebras, a crucial role is played by a family of integer vectors, called c-vectors, which parametrize the coefficients. It has recently been shown that each c-vector with respect to an acyclic initial seed is a real root of the corresponding root system. In this paper, we obtain an interpretation of this result in terms of symmetric matrices. We show that for skew-symmetric cluster algebras, the c-vectors associated with any seed defines a quasi-Cartan companion for the corresponding exchange matrix (i. e. they form a companion basis), and we establish some basic combinatorial properties. In particular, we show that these vectors define an admissible cut of edges in the associated quivers.
Subject Keywords
Tilted Algebras
,
Quivers
URI
https://hdl.handle.net/11511/55361
Journal
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Collections
Department of Mathematics, Article
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A. İ. Seven, “CLUSTER ALGEBRAS AND SYMMETRIC MATRICES,”
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
, pp. 469–478, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/55361.