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Triangulated categories and Kac-Moody algebras
Authors:Liangang Peng  Jie Xiao
Institution:Department of Mathematics, Sichuan University, 610064 Chengdu, PR China?(e-mail: penglg@mail.sc.cninfo.net), CN
Department of Mathematics, Tsinghua University, 100084 Beijing, PR China?(e-mail: jxiao@math.tsinghua.edu.cn), CN
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. Oblatum 4-XII-1998 & 11-XI-1999?Published online: 21 February 2000
Keywords:Mathematics Subject Classification (1991): 16G20  17B67  Secondary 16G10  17B37
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