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.
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.
出处
《数学的实践与认识》
CSCD
北大核心
2011年第4期176-181,共6页
Mathematics in Practice and Theory
基金
河北省自然科学基金(A2010000194)
保定市科技攻关计划项目(10ZG009)
关键词
李三系
Frattini子系
幂零李三系
基本李三系
Lie triple system
the Frattini subsystem
Nilpotent Lie triple system
Elementary Lie triple system
