Mutation Classes of 3 x 3 Generalized Cartan Matrices
HIGHLIGHTS IN LIE ALGEBRAIC METHODS, vol.295, pp.205-211, 2012 (Scopus)
- Publication Type: Article / Article
- Volume: 295
- Publication Date: 2012
- Doi Number: 10.1007/978-0-8176-8274-3_9
- Journal Name: HIGHLIGHTS IN LIE ALGEBRAIC METHODS
- Journal Indexes: Scopus, zbMATH
- Page Numbers: pp.205-211
- Middle East Technical University Affiliated: Yes
Abstract
One of the recent developments in representation theory has been the introduction of cluster algebras by Fomin and Zelevinsky. It is now well known that these algebras are closely related with different areas of mathematics. A particular analogy exists between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices, while Kac-Moody algebras correspond to (symmetrizable) generalized Caftan matrices. In this paper, we describe an interplay between these two classes of matrices in size 3. In particular, we give a characterization of the mutation classes associated with the generalized Cartan matrices of size 3, generalizing results of Beineke-Bruestle-Hille.