[1]周建华.一类李代数的结构[J].东南大学学报(自然科学版),1989,19(5):38-45.[doi:10.3969/j.issn.1001-0505.1989.05.006]
 Zhou Jianhua (Department of Mathematics and Mechanics).The Structure of a Class of Lie Algebras[J].Journal of Southeast University (Natural Science Edition),1989,19(5):38-45.[doi:10.3969/j.issn.1001-0505.1989.05.006]
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一类李代数的结构()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
19
期数:
1989年第5期
页码:
38-45
栏目:
本刊信息
出版日期:
1989-09-20

文章信息/Info

Title:
The Structure of a Class of Lie Algebras
作者:
周建华
东南大学数学力学系
Author(s):
Zhou Jianhua (Department of Mathematics and Mechanics)
关键词:
可解 幂零 共轭/自中心ad幂零
Keywords:
Soluble nilpotent cojugate/self-centralization nilpotent
分类号:
+
DOI:
10.3969/j.issn.1001-0505.1989.05.006
摘要:
本文讨论含元x使(adx)^{dimL-1}=0但(adx)^{dimL-2}≠0的特征零李代数L的结构,利用关于可解李代数的结论,对这种不可解李代数进行了完全分类;还证明了,在这样的代数中,这些元素在AutL下是相互共轭的(允许相差一非零常数倍)。
Abstract:
This paper discusses the structure of characteristic zero Lie algebra L which contains an clement x such that (adx)^{dimL-1}=0 but (adx)^{dimL-2}≠0. Based on the results of soluble algebras, the nonsoluble algebras are classified. It is also proved that such elements in such algebra are all conjugate under Aut L, up to nonzero scalar multiples.
更新日期/Last Update: 2013-04-30