1. 3-Derivations and 3-Automorphisms on Lie Algebras.
- Author
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Xia, Haobo
- Subjects
- *
LIE algebras , *GROUP algebras , *LIE groups , *DIFFERENTIAL algebra , *STEINER systems - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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