Mutation classes of finite type cluster algebras with principal coefficients

Seven A. İ.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.438, pp.4584-4594, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 438
  • Publication Date: 2013
  • Doi Number: 10.1016/j.laa.2013.02.025
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.4584-4594
  • Keywords: Cluster algebras, Mutation classes, Skew-symmetrizable matrices
  • Middle East Technical University Affiliated: Yes

Abstract

Cluster algebras of finite type is a fundamental class of algebras whose classification is identical to the famous Cartan Killing classification. More recently, Fomin and Zelevinslcy introduced another central notion of cluster algebras with principal coefficients. These algebras are determined combinatorially by mutation classes of certain rectangular matrices. It was conjectured, by Fomin and Zelevinsky, that finite type cluster algebras with principal coefficients are characterized by the mutation classes which are finite. In this paper, we prove this conjecture. (C) 2013 Elsevier Inc. All rights reserved.