Mutation classes of finite type cluster algebras with principal coefficients

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.


Quivers of finite mutation type and skew-symmetric matrices
Seven, Ahmet İrfan (Elsevier BV, 2010-11-01)
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 ...
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Citation Formats
A. İ. Seven, “Mutation classes of finite type cluster algebras with principal coefficients,” LINEAR ALGEBRA AND ITS APPLICATIONS, pp. 4584–4594, 2013, Accessed: 00, 2020. [Online]. Available: