Quivers of finite mutation type and skew-symmetric matrices

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Seven A. İ.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.433, pp.1154-1169, 2010 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 433
  • Publication Date: 2010
  • Doi Number: 10.1016/j.laa.2010.04.043
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1154-1169
  • Keywords: Quiver mutation, Finite mutation type, Skew-symmetric matrix
  • Middle East Technical University Affiliated: Yes


Quivers of finite mutation type are certain directed graphs that first arised in Fomin-Zelevinsky's theory of cluster algebras. It has been observed that these quivers are also closely related with different areas of mathematics. In fact, main examples of finite mutation type quivers are the quivers associated with triangulations of surfaces. In this paper, we study structural properties of finite mutation type quivers in relation with the corresponding skew-symmetric matrices. We obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical invariant for their mutation classes. (C) 2010 Elsevier Inc. All rights reserved.