| 四元数辛李代数MAD子代数的共轭性 |
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| 引用本文： | 李秀仙,靳全勤,安慧辉.四元数辛李代数MAD子代数的共轭性[J].河海大学学报(自然科学版),2015(3):335-344. |
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| 作者姓名： | 李秀仙 靳全勤 安慧辉 |
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| 作者单位： | 天津商业大学理学院, 天津 300134.,通讯作者. 同济大学数学系, 上海 200092.,辽宁师范大学数学学院, 辽宁 大连 116069. |
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| 基金项目： | 本文受到国家自然科学基金(No.11071187)和天津商业大学青年基金 (No.140112)的资助. |
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| 摘 要： | 利用四元数理论, 证明了四元数体上辛李代数为实半单李代数, 其极大可交换ad-\!\!可对角化(简称MAD)子代数是相互共轭的.
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| 关 键 词： | 四元数 辛李代数 MAD子代数 共轭 |
Conjugacy of the MAD Subalgebras for Symplectic Lie
Algebras over the Quaternions |
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| LI XiuxianJIN,Quanqin and AN Huihui.Conjugacy of the MAD Subalgebras for Symplectic Lie
Algebras over the Quaternions[J].Journal of Hohai University (Natural Sciences ),2015(3):335-344. |
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| Authors: | LI XiuxianJIN Quanqin and AN Huihui |
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| Institution: | College of Science, Tianjin University of Commerce, Tianjin 300134, China.,Corresponding author. Department of Mathematics, Tongji University, Shang-
hai 200092, China. and School of Mathematics, Liaoning Normal University, Dalian 116069, Liaoning,
China. |
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| Abstract: | Using the theory of quaternion matrices, the authors prove that the symplectic
Lie algebras over the quaternions are real semisimple Lie algebras, and their maximal abelian
ad-diagonalizable (MAD for short) subalgebras are all conjugate. |
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| Keywords: | Quaternions Symplectic Lie algebras MAD subalgebras Conjugate |
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