Cluster algebras of finite type and positive symmetrizable matrices

• Autores: Michael Barot, Christof Geiss, Andrei Zelevinsky
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 73, Nº 3, 2006, págs. 545-564
• Idioma: inglés
• DOI: 10.1112/s0024610706022769
• Texto completo no disponible (Saber más ...)
• Resumen

  • The paper is motivated by an analogy between cluster algebras and Kac-Moody algebras: both theories share the same classification of finite type objects by familiar Cartan-Killing types. However, the underlying combinatorics beyond the two classifications is different: roughly speaking, Kac-Moody algebras are associated with (symmetrizable) Cartan matrices, while cluster algebras correspond to skew-symmetrizable matrices. We study an interplay between the two classes of matrices, in particular, establishing a new criterion for deciding whether a given skew-symmetrizable matrix gives rise to a cluster algebra of finite type.