MUTATION CLASSES OF SKEW-SYMMETRIZABLE 3 x 3 MATRICES

Date

2013-05-01

Author

Seven, Ahmet İrfan

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Mutation of skew-symmetrizable matrices is a fundamental operation that first arose in Fomin-Zelevinsky's theory of cluster algebras; it also appears naturally in many different areas of mathematics. In this paper, we study mutation classes of skew-symmetrizable 3 x 3 matrices and associated graphs. We determine representatives for these classes using a natural minimality condition, generalizing and strengthening results of Beineke-BrustleHille and Felikson-Shapiro-Tumarkin. Furthermore, we obtain a new numerical invariant for the mutation operation on skew-symmetrizable matrices of arbitrary size.

Subject Keywords

Cluster algebras II, Finite-type

URI

https://hdl.handle.net/11511/54786

Journal

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

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Department of Mathematics, Article

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Citation Formats

A. İ. Seven, “MUTATION CLASSES OF SKEW-SYMMETRIZABLE 3 x 3 MATRICES,” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, pp. 1493–1504, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54786.