分裂的δ-JORDAN李三系的结构  

ON THE STRUCTURE OF SPLIT δ-JORDAN LIE TRIPLE SYSTEMS

作　　者：曹燕 CAO Yan(Department of Mathematics,School of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院数学系,黑龙江哈尔滨150080

出　　处：《数学杂志》2020年第3期314-322,共9页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11801121);NSF of Heilongjiang Province(QC2018006);the Fundamental Research Fundation for Universities of Heilongjiang Province(LGYC2018JC002)。

摘　　要：本文研究了带有相关0根空间的任意分裂的δ-Jordan李三系的结构.利用这种三系的根连通,得到了带有对称根系的分裂的δ-Jordan李三系T可以表示成T=U+∑[α]∈∧^1/~I[α],其中U是0根空间T0的子空间,任意I[α]为T的理想,并且满足当[α]≠[β]时,[I[α],T,I[β]]=0.The aim of this article is to study the structure of arbitrary split δ-Jordan Lie triple systems by focussing on those with a coherent 0-root space.By developing techniques of connections of roots for this kind of triple system T,we show that such an arbitrary δ-JLTS with a symmetric root system is of the form T=U+∑[α]∈∧^1/~I[α]with U a subspace of the 0-root space T0 and any I[α]a well described ideal of T,satisfying[I[α],T,I[β]]=0 if[α]≠[β].

关 键 词：分裂的δ-Jordan李三系 李三系 δ-Jordan李代数 根系 根空间 

分 类 号：O152.5[理学—数学]