J. Korean Math. Soc. 2017; 54(4): 1265-1279
Online first article April 3, 2017 Printed July 1, 2017
https://doi.org/10.4134/JKMS.j160465
Copyright © The Korean Mathematical Society.
Yan Cao and Liangyun Chen
Harbin University of Science and Technology, Northeast Normal University
In order to study the structure of arbitrary split Leibniz triple systems, we introduce the class of split Leibniz triple systems as the natural extension of the class of split Lie triple systems and split Leibniz algebras. By developing techniques of connections of roots for this kind of triple systems, we show that any of such Leibniz triple systems $T$ with a symmetric root system is of the form $T=U+\sum_{[j]\in \Lambda^{1}/\sim} I_{[j]}$ with $U$ a subspace of $T_{0}$ and any $I_{[j]}$ a well described ideal of $T$, satisfying $\{I_{[j]},T,I_{[k]}\} =\{I_{[j]},I_{[k]},T\}=\{T,I_{[j]},I_{[k]}\}=0$ if $[j]\neq [k]$.
Keywords: split Leibniz triple system, Lie triple system, Leibniz algebra, root system, root space
MSC numbers: 17B75, 17A60, 17B22, 17B65
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