Publication details for Pavel TumarkinFelikson, A., Shapiro, M. & Tumarkin, P. (2012). Cluster algebras of finite mutation type via unfoldings. International Mathematics Research Notices 2012(8): 1768-1804.
- Publication type: Journal Article
- ISSN/ISBN: 1073-7928, 1687-0247
- DOI: 10.1093/imrn/rnr072
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
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.