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Cluster algebras of finite mutation type via unfoldings.

Felikson, A. and Shapiro, M. and Tumarkin, P. (2012) 'Cluster algebras of finite mutation type via unfoldings.', International mathematics research notices., 2012 (8). pp. 1768-1804.

Abstract

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.1093/imrn/rnr072
Publisher statement:This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Felikson, A., Shapiro, M. and Tumarkin, P. (2012) 'Cluster algebras of finite mutation type via unfoldings.', International mathematics research notices., 2012 (8): 1768-1804 is available online at: http://dx.doi.org/10.1093/imrn/rnr072
Record Created:03 Feb 2016 14:05
Last Modified:03 Feb 2016 14:10

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