| On Split $\delta$-Jordan Lie Triple Systems |
| Received:January 23, 2019 Revised:September 04, 2019 |
| Key Words:
split $\delta$-Jordan Lie triple system Lie triple system root system
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11801121), the Natural Science Foundation of Heilongjiang Province (Grant No.QC2018006) and the Fundamental Research Fundation for Universities of Heilongjiang Province (Grant No.LGYC2018JC002). |
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| Abstract: |
| 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 $[\alpha]\neq [\beta]$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2020.02.003 |
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