On Split δ-Jordan Lie Triple Systems  

作　　者：Yan CAO Liangyun CHEN 

机构地区：[1]Department of Mathematics.Harbin University of Science and Technology,Heilongjiang 150080,P.R.China [2]School of Mathematics and Statistics,Northeast Normal University,Jilin 130024,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2020年第2期127-139,共13页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11801121);the Natural Science Foundation of Heilongjiang Province(Grant No.QC2018006);the Fundamental Research Fundation for Universities of Heilongjiang Province(Grant No.LGYC2018JC002).

摘　　要：The aim of this article is to study the structures of arbitrary split δ-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 δ-Jordan Lie triple systems T with a symmetric root system is of the form T=U+∑[α]∈■1/~I[α] with U a subspace of T0 and any I[α] a well described ideal of T, satisfying{I[α],T,I[β]}={I[α],I[β],T}={T,I[α],I[β]}=0 if [α]≠[β] .The aim of this article is to study the structures of arbitrary split δ-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 δ-Jordan Lie triple systems T with a symmetric root system is of the form ■with U a subspace of T0 and any I[α] a well described ideal of T, satisfying■ .

关 键 词：splitδ-Jordan LIE TRIPLE SYSTEM LIE TRIPLE SYSTEM ROOT SYSTEM 

分 类 号：O152.5[理学—数学]