具有有限多个理想的李代数  

Lie Algebras with a Finite Number of Ideals

作　　者：吴月柱[1] 孟道骥[2] 

机构地区：[1]曲阜师范大学数学系,山东曲阜273165 [2]南开大学数学系,天津300071

出　　处：《数学学报（中文版）》2002年第6期1197-1206,共10页Acta Mathematica Sinica：Chinese Series

摘　　要：本文给出了复数域C上的具有有限多个理想的有限维李代数L的结构:L=S+ Cr+ N,其中 S为 Levi因子,Cr+N为根基,N为幂零根基.当 N为交换时,文中还给出具有这种结构的李代数L具有有限多个理想的充要条件,并且将N为Heisenberg代数或亚交换李代数的惰形的讨论归结为N是交换的情形.Abstract Let L be a finite dimensional Lie algebra with a finite number of ideals over the complex number field. The paper obtains the struture of L. And the paper studies the Lie algebra L such that L = S + Cr + N, [S,r] = 0: When N is abelian, the sufficient and necessary conditions under which L has a finite number of ideals are found; when N is a Heisenberg algebra or metabelian algebra, the paper simplifies the problem to the case where N is abelian.

关 键 词：理想 李代数 Levi分解 根基 幂零根基 半单线性变换 

分 类 号：O152.5[理学—数学]