3-Derivations and 3-Automorphisms on Lie Algebras

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 deri...

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Bibliographic Details
Published in:Mathematics
Main Author: Haobo Xia
Format: Article
Language:English
Published: MDPI AG 2022-02-01
Subjects:
Lie algebra
3-derivation
3-automorphism
exponential map
Online Access:https://www.mdpi.com/2227-7390/10/5/782
Description
Summary: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.
ISSN:2227-7390

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