Cluster algebras of finite mutation type via unfoldings

Details Cluster algebras of finite mutation type via unfoldings Cluster algebras of finite mutation type via unfoldings

2010-06-22

arxiv.org/abs/1006.4276v4

Mathematics

Combinatorics

40 pages, a lot of figures

Scientific paper

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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