3-Derivations and 3-Automorphisms on Lie Algebras

Haobo Xia
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Haobo Xia: Department of Mathematics, Jilin University, Changchun 130012, China

Mathematics, 2022, vol. 10, issue 5, 1-12

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.

Keywords: Lie algebra; 3-derivation; 3-automorphism; exponential map (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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