Cluster algebras of finite mutation type via unfoldings

By Anna Felikson, Michael Shapiro, Pavel Tumarkin. 2010

97 citations recorded by the source corpus.

We complete classification of mutation-finite cluster algebras by extending the technique derived by Fomin, Shapiro, and Thurston to skew-symmetrizable case. We show that for every mutation-finite skew-symmetrizable matrix a diagram characterizing the matrix admits an unfolding which embeds its mutation class to the mutation class of some mutation-finite skew-symmetric matrix. In particular, this establishes a correspondence between a large class of skew-symmetrizable mutation-finite cluster algebras and triangulated marked bordered surfaces.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/57567985738a656b18dea328b6054a09dd0f6d10

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In Algebra and Number Theory

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Citations in the corpus

Snake graph calculus and cluster algebras from surfaces II: self-crossing snake graphs (2014, background): “For generalizations to the skew-symmetrizable case see [7,8].”
Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths (2012, methodology): “From the standpoint of general structure theory of cluster algebras, the importance of the surface case studied in this paper and its prequel [9] was validated by the classification of cluster algebras of finite mutation type obtained in [36, 37].”