Maximal green sequences of skew-symmetrizable 3 x 3 matrices

Seven A. İ.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.440, pp.125-130, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 440
  • Publication Date: 2014
  • Doi Number: 10.1016/j.laa.2013.10.018
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.125-130
  • Middle East Technical University Affiliated: Yes

Abstract

Maximal green sequences are particular sequences of mutations of skew-symmetrizable matrices which were introduced by Keller in the context of quantum dilogarithm identities and independently by Cecotti-Cordova-Vafa in the context of supersymmetric gauge theory. In this paper we study maximal green sequences of skew-symmetrizable 3 x 3 matrices. We show that such a matrix with a mutation-cyclic diagram does not have any maximal green sequence. We also obtain some basic properties of maximal green sequences of skew-symmetrizable matrices with mutation-acyclic diagrams. (C) 2013 Elsevier Inc. All rights reserved.