On Split $\delta$-Jordan Lie Triple Systems

DOI：10.3770/j.issn:2095-2651.2020.02.003

 作者 单位 曹燕 哈尔滨理工大学理学院, 黑龙江 哈尔滨 150080 陈良云 东北师范大学数学与统计学院, 吉林 长春 130024

本文研究了任意分裂的$\delta$-Jordan李三系的结构,其为分裂的李三系的结构的推广. 利用这种三系的根连通, 得到了带有对称根系的分裂的 $\delta$-Jordan 李三系可以表示成 $T=U+\sum_{[\alpha]\in \Lambda^{1}/\sim} I_{[\alpha]}$,其中$U$是0根空间$T_{0}$的子空间,任意$I_{[\alpha]}$为$T$的理想, 并且满足 当$[\alpha]\neq [\beta]$时, $\{I_{[\alpha]},T,I_{[\beta]}\}=\{I_{[\alpha]},I_{[\beta]},T\}=\{T,I_{[\alpha]},I_{[\beta]}\}=0$.

The aim of this article is to study the structures of arbitrary split $\delta$-Jordan Lie triple systems, which are a generalization of split Lie triple systems. By developing techniques of connections of roots for this kind of triple systems, we show that any of such $\delta$-Jordan Lie triple systems $T$ with a symmetric root system is of the form $T=U+\sum_{[\alpha]\in \Lambda^{1}/\sim} I_{[\alpha]}$ with $U$ a subspace of $T_{0}$ and any $I_{[\alpha]}$ a well described ideal of $T$, satisfying $\{I_{[\alpha]},T,I_{[\beta]}\}=\{I_{[\alpha]},I_{[\beta]},T\}=\{T,I_{[\alpha]},I_{[\beta]}\}=0$ if $[\alpha]\neq [\beta]$.