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3-Derivations and 3-Automorphisms on Lie Algebras

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  • Haobo Xia

    (Department of Mathematics, Jilin University, Changchun 130012, China)

Abstract

In this paper, first we establish the explicit relation between 3-derivations and 3- automorphisms of a Lie algebra using the differential and exponential map. More precisely, we show that the Lie algebra of 3-derivations is the Lie algebra of the Lie group of 3-automorphisms. Then we study the derivations and automorphisms of the standard embedding Lie algebra of a Lie triple system. We prove that derivations and automorphisms of a Lie triple system give rise to derivations and automorphisms of the corresponding standard embedding Lie algebra. Finally we compute the 3-derivations and 3-automorphisms of 3-dimensional real Lie algebras.

Suggested Citation

  • Haobo Xia, 2022. "3-Derivations and 3-Automorphisms on Lie Algebras," Mathematics, MDPI, vol. 10(5), pages 1-12, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:782-:d:761372
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