We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

Skew-symmetric cluster algebras of finite mutation type.

Felikson, A. and Shapiro, M. and Tumarkin, P. (2012) 'Skew-symmetric cluster algebras of finite mutation type.', Journal of the European Mathematical Society., 14 (4). pp. 1135-1180.


In the famous paper [FZ2] Fomin and Zelevinsky obtained Cartan-Killing type classification of all cluster algebras of finite type, i.e. cluster algebras having only finitely many distinct cluster variables. A wider class of cluster algebras is formed by cluster algebras of finite mutation type which have finitely many exchange matrices (but are allowed to have infinitely many cluster variables). In this paper we classify all cluster algebras of finite mutation type with skew-symmetric exchange matrices. Besides cluster algebras of rank 2 and cluster algebras associated with triangulations of surfaces there are exactly 11 exceptional skew-symmetric cluster algebras of finite mutation type. More precisely, 9 of them are associated with root systems E6, E7, E8, E˜6, E˜7, E˜8, E(1,1)6, E(1,1)7, E(1,1)8; two remaining were found by Derksen and Owen in [DO]. We also describe a criterion which determines if a skew-symmetric cluster algebra is of finite mutation type, and discuss growth rate of cluster algebras.

Item Type:Article
Keywords:Cluster algebra, Finite mutation type, Triangulated surface, Growth rate.
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Record Created:03 Feb 2016 14:05
Last Modified:04 Feb 2016 12:42

Social bookmarking: del.icio.usConnoteaBibSonomyCiteULikeFacebookTwitterExport: EndNote, Zotero | BibTex
Look up in GoogleScholar | Find in a UK Library