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arXiv · 1412.7804

Generalized Derivations of Lie triple systems

Jia Zhou·Liangyun Chen·Yao Ma
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Abstract

In this paper, we present some basic properties concerning the derivation algebra ${\rm Der}(T)$, the quasiderivation algebra ${\rm QDer}(T)$ and the generalized derivation algebra ${\rm GDer}(T)$ of a Lie triple system $T$, with the relationship ${\rm Der}(T)\subseteq {\rm QDer}(T)\subseteq {\rm GDer}(T)\subseteq {\rm End}(T)$. Furthermore, we completely determine those Lie triple systems $T$ with condition ${\rm QDer}(T)={\rm End}(T)$. We also show that the quasiderivations of $T$ can be embedded as derivations in a larger Lie triple system.

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Jia Zhou, Liangyun Chen, Yao Ma. 2014-12-25. Generalized Derivations of Lie triple systems. https://arxiv.org/abs/1412.7804

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