Rigid modules over preprojective algebras

• 成果类型: Article
• 署名作者: Geiss, Christof; Leclerc, Bernard; Schroeer, Jan
• 署名单位: University of Bonn; Universidad Nacional Autonoma de Mexico; Universite de Caen Normandie
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-006-0507-y
• 发表日期: 2006
• 页码: 589-632
• 关键词: semicanonical bases

摘要

Let Lambda be a preprojective algebra of simply laced Dynkin type Delta. We study maximal rigid Lambda-modules, their endomorphism algebras and a mutation operation on these modules. This leads to a representation-theoretic construction of the cluster algebra structure on the ring C[N] of polynomial functions on a maximal unipotent subgroup N of a complex Lie group of type Delta. As an application we obtain that all cluster monomials of C[N] belong to the dual semicanonical basis.