Triangulated categories and Kac-Moody algebras

• 成果类型: Article
• 署名作者: Peng, LG; Xiao, J
• 署名单位: Sichuan University; Tsinghua University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s002220000062
• 发表日期: 2000
• 页码: 563-603
• 关键词: quantum groups; hereditary algebras; hall polynomials; lie-algebras; Finite; REPRESENTATIONS

摘要

By using the Ringel-Hall algebra approach, we find a Lie algebra arising in each triangulated category with T-2 = 1, where T is the translation functor, In particular, the generic form of the Lie algebras determined by the root categories, the 2-period orbit categories of the derived categories of finite dimensional hereditary associative algebras, gives a realization of all symmetrizable Kac-Moody Lie algebras.