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Cluster algebras of finite mutation type via unfoldings

Felikson, A.; Shapiro, M.; Tumarkin, P.

Cluster algebras of finite mutation type via unfoldings Thumbnail


M. Shapiro


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.


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

Journal Article Type Article
Publication Date Jan 1, 2012
Deposit Date Mar 19, 2012
Publicly Available Date Feb 3, 2016
Journal International Mathematics Research Notices
Print ISSN 1073-7928
Electronic ISSN 1687-0247
Publisher Oxford University Press
Peer Reviewed Peer Reviewed
Volume 2012
Issue 8
Pages 1768-1804


Accepted Journal Article (345 Kb)

Copyright 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:

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