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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Pavel Tumarkin

Felikson, A., Shapiro, M. & Tumarkin, P. (2012). Cluster algebras of finite mutation type via unfoldings. International Mathematics Research Notices 2012(8): 1768-1804.

Author(s) from Durham


We complete the 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.