CLUSTER ALGEBRAS AND SEMIPOSITIVE SYMMETRIZABLE MATRICES
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol.363, pp.2733-2762, 2011 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 363
- Publication Date: 2011
- Doi Number: 10.1090/s0002-9947-2010-05255-9
- Journal Name: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.2733-2762
- Open Archive Collection: AVESIS Open Access Collection
- Middle East Technical University Affiliated: Yes
Abstract
There is a particular analogy 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 Cartan matrices. Both classes of algebras and the associated matrices have the same classification of finite type objects by the well-known Cartan-Killing types. In this paper, we study an extension of this correspondence to the affine type. In particular, we establish the cluster algebras which are determined by the generalized Cartan matrices of affine type.