限制李三系的型心  

Centroids of Restricted Lie Triple Systems

作　　者：刘艳培 董艳芹 周涵琪 丛昕 Liu Yanpei;Dong Yanqin;Zhou Hanqi;Cong Xin(College of Mathematics,Changchun Normal University,Changchun 130032,China)

机构地区：[1]长春师范大学数学学院,吉林长春130032

出　　处：《洛阳师范学院学报》2023年第8期12-15,47,共5页Journal of Luoyang Normal University

基　　金：国家自然科学基金资助项目(11171055);吉林省教育厅科学技术研究项目(JJKH20220823KJ);长春师范大学自然科学基金资助项目([2018]008)。

摘　　要：给出了限制李三系型心及拟型心的定义,研究了它们之间的结构关系.证明了限制李三系所有线性变换构成的集合End(T)为限制李三系、限制李三系型心和拟型心构成的集合为End(T)的p-子系;进而证明了限制李三系中心为零时,限制李三系的型心和拟型心可以分解为其p-理想的直和;在此基础上,给出了限制李三系中心为零时,若D∈C(T),则Im(D)和Ker(D)是T的p-理想.This research defined quasicentroid and centroid of restricted Lie triple systems and explored their structural relations.The result shows that the set End(T)consisting of all linear transformations of restricted Lie triple systems should be p-subsystem of End(T),which constructs restricted Lie triple systems and their quasicentroid and centroid.This research also shows that the quasicentroid and centroid can be decomposed into the direct sum of two p-ideals when the center of restricted Lie triple systems is zero.Furthermore,when the center of restricted Lie triple systems is zero,if D∈C(T),then Im(D)and Ker(D)are p-ideals of T.

关 键 词：限制李三系 型心 导子 

分 类 号：O152.5[理学—数学]