From triangulated categories to cluster algebras

• 成果类型: Article
• 署名作者: Caldero, Philippe; Keller, Bernhard
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet; Universite Paris Cite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-008-0111-4
• 发表日期: 2008
• 页码: 169-211
• 关键词: hall algebras; QUIVERS; REPRESENTATIONS

摘要

The cluster category is a triangulated category introduced for its combinatorial similarities with cluster algebras. We prove that a cluster algebra A of finite type can be realized as a Hall algebra, called exceptional Hall algebra, of the cluster category. This realization provides a natural basis for A. We prove new results and formulate conjectures on ` good basis' properties, positivity, denominator theorems and toric degenerations.