Maximal green sequences of skew-symmetrizable 3 x 3 matrices


Seven A. İ.

LINEAR ALGEBRA AND ITS APPLICATIONS, cilt.440, ss.125-130, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 440
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.laa.2013.10.018
  • Dergi Adı: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Sayfa Sayıları: ss.125-130

Özet

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.