The present paper deals with the Lie triple systems via Leibniz algebras. A perfect Lie algebra as a perfect Leibniz algebra and as a perfect Lie triple system is considered and the appropriate universal central extensions are studied. Using properties of Leibniz algebras, it is shown that the Lie triple system universal central extension is either the universal central extension of the Leibniz algebra or the universal central extension of the Lie algebra.

中文翻译：

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李三重系统和莱布尼兹代数

本文通过Leibniz代数处理Lie三重系统。考虑了理想的李代数，理想的莱布尼兹代数和理想的李三重系统，并研究了适当的通用中心扩展。利用Leibniz代数的性质，证明了李三重系统的通用中心扩展是Leibniz代数的通用中心扩展或Lie代数的通用中心扩展。