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arXiv · 1006.4276

Cluster algebras of finite mutation type via unfoldings

Anna Felikson·Michael Shapiro·Pavel Tumarkin
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Abstract

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.

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Anna Felikson, Michael Shapiro, Pavel Tumarkin. 2011-03-06. Cluster algebras of finite mutation type via unfoldings. https://doi.org/10.1093/imrn%2Frnr072

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