Inventiones mathematicae

, Volume 140, Issue 3, pp 563–603 | Cite as

Triangulated categories and Kac-Moody algebras

  • Liangang Peng
  • Jie Xiao


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.

Mathematics Subject Classification (1991): 16G20, 17B67; Secondary 16G10, 17B37 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Liangang Peng
    • 1
  • Jie Xiao
    • 2
  1. 1.Department of Mathematics, Sichuan University, 610064 Chengdu, PR China¶(e-mail:
  2. 2.Department of Mathematics, Tsinghua University, 100084 Beijing, PR China¶(e-mail:

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