Abstract.
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.
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Oblatum 4-XII-1998 & 11-XI-1999¶Published online: 21 February 2000
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Peng, L., Xiao, J. Triangulated categories and Kac-Moody algebras. Invent. math. 140, 563–603 (2000). https://doi.org/10.1007/s002220000062
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DOI: https://doi.org/10.1007/s002220000062