| 一类李代数的结构 |
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| 引用本文： | 张海山,卢才辉.一类李代数的结构[J].数学学报,1998,41(5):1075-1078. |
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| 作者姓名： | 张海山 卢才辉 |
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| 作者单位： | 首都师范大学数学系 |
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| 基金项目： | 国家自然科学基金,北京市自然科学基金 |
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| 摘 要： | 本文给出了复数域Ｃ上具有有限多个理想的有限维非可解李代数的结构为Ｌ＝Ｃｒ○＋Ｎ○＋Ｓ，其中Ｓ是Ｌ的Ｌｅｖｉ因子，Ｎ是Ｌ的幂零根基，Ｃｒ○＋Ｎ是Ｌ的根基，ａｄｒ是Ｎ的半单纯线性变换，［ｒ，Ｓ］＝０；还给出了这类李代数的一些重要性质．
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| 关 键 词： | Levi分解，Levi因子，根基，半单李代数 |
The Structure of a Kind of Lie Algebra |
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| Zhang Haishan,Lu Caihui.The Structure of a Kind of Lie Algebra[J].Acta Mathematica Sinica,1998,41(5):1075-1078. |
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| Authors: | Zhang Haishan Lu Caihui |
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| Institution: | Zhang Haishan Lu Caihui (Department of Mathematics, Capital Normal University, Beijing 100037, China) |
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| Abstract: | Let L be a finite dimensional unsovable Lie algebra with finite number of ideals over the complex number field C. The paper obtained the structure and some important properties ofL. In addition, we give the sufficient and necessary condition underwhich a nilpotent Lie algebra has finite number of ideals. |
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| Keywords: | Levi decomposition Levi factor Radical Semisimple Lie algebra |
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