MUTATION CLASSES OF SKEW-SYMMETRIZABLE 3 x 3 MATRICES

Seven A. İ.

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.141, pp.1493-1504, 2013 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 141
  • Publication Date: 2013
  • Journal Name: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1493-1504
  • Middle East Technical University Affiliated: Yes

Abstract

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.