| 三维实李代数的分类 |
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| 引用本文： | 胡建华,栗菲菲,刘静.三维实李代数的分类[J].上海理工大学学报,2020,42(3):220-223. |
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| 作者姓名： | 胡建华 栗菲菲 刘静 |
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| 作者单位： | 上海理工大学理学院,上海 200093;上海理工大学理学院,上海 200093;上海理工大学理学院,上海 200093 |
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| 基金项目： | 上海理工大学教师教学发展研究基金资助项目（LXYJY07） |
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| 摘 要： | 根据李代数的导代数的性质及同构条件完成三维实李代数的分类。当导代数维数为0和1时,由李括号运算的性质及基的变换可将李代数分为三类:L (3,0),L (3,-1),L (3,1)。当导代数维数为2和3时,根据内导子对应矩阵特征值的性质可将李代数分为五类:L (3,2,a),L (3,3),L (3,4,c),L (3,5),L (3,6)。
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| 关 键 词： | 李代数 导代数 同构 |
| 收稿时间： | 2019/4/16 0:00:00 |
Classification of three-dimensional real Lie algebra |
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| HU Jianhu,LI Feifei,LIU Jing.Classification of three-dimensional real Lie algebra[J].Journal of University of Shanghai For Science and Technology,2020,42(3):220-223. |
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| Authors: | HU Jianhu LI Feifei LIU Jing |
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| Institution: | College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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| Abstract: | The classification of three-dimensional real Lie algebra was completed according to the properties of derivative algebras and isomorphic conditions of Lie algebra. When the dimension of derivative algebra is 0 or 1, Lie algebra can be divided into three types, $ L\left( {3,0} \right)$, $ L\left( {3, - 1} \right)$ and $ L\left( {3,1} \right)$, according to the properties of Lie bracket operation and the transformation of basis.When the dimension of derivative algebra is 2 or 3, Lie algebras can be divided into five types, $ L\left( {3,2,a} \right)$, $ L\left( {3,3} \right)$, $ L\left( {3,4,c} \right)$, $ L\left( {3,5} \right)$, $ L\left( {3,6} \right)$, according to the properties of eigenvalues of matrix corresponding to internal derivations. |
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| Keywords: | Lie algebra derivative algebra isomorphism |
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