| 李三系的Frattini子系 |
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| 引用本文： | 白喜梅,白瑞蒲,赵胜光.李三系的Frattini子系[J].数学的实践与认识,2011,41(4). |
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| 作者姓名： | 白喜梅 白瑞蒲 赵胜光 |
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| 作者单位： | 1. 河北大学,数学与计算机学院,河北,保定,071002
2. 中国冶金总局,地球物理勘察院,河北,保定,071051 |
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| 基金项目： | 河北省自然科学基金(A2010000194); 保定市科技攻关计划项目(10ZG009) |
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| 摘 要： | 李三系是从黎曼对称空间产生的三元运算的代数系统,近年来备受数学家们的重视.针对李三系的Frattini子系和基本李三系的问题进行了研究,给出了Frattini子系和基本李三系的一些性质,并证明了李三系的非嵌入定理,同时得到了幂零李三系是基本李三系的一个充要条件.
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| 关 键 词： | 李三系 Frattini子系 幂零李三系 基本李三系 |
The Frattini subsystem of Lie Triple Systems |
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| BAI Xi-mei,BAI Rui-pu,ZHAO Sheng-guang.The Frattini subsystem of Lie Triple Systems[J].Mathematics in Practice and Theory,2011,41(4). |
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| Authors: | BAI Xi-mei BAI Rui-pu ZHAO Sheng-guang |
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| Institution: | BAI Xi-mei~1,BAI Rui-pu~1,ZHAO Sheng-guang~2 (1.Department of Mathmatics and Computer,Hebei University,Baoding 071002,China) (2.Institute of Geophysical Survey of China,Metallurgical Geology Bureau,Baoding 071051,China) |
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| Abstract: | Lie triple system is an algebraic system with a ternary composition abstracted from Rienannian symmetric space and is paid to close attention by mathematicians.In this paper,we mainly study some properties of the Frattini subsystem of Lie triple systems and elementary Lie triple systems.We also give the non-imbedding theorem of Lie triple system. At the same time,the necessary and sufficient condition for a nilpotent Lie triple system to be an elementary Lie triple system is obtained. |
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| Keywords: | Lie triple system the Frattini subsystem Nilpotent Lie triple system Elementary Lie triple system |
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