3-derivations And 3-automorphisms Of Lie Algebras

In this paper,using the method of differential and exponential map,we show that the 3-derivation Lie algebra of a Lie algebra is the Lie algebra of the 3-automorphism Lie group of the Lie algebra.We establish the ex-plicit relation between 3-derivations and 3-automorphisms of a Lie algebra.And we study the derivations and automorphisms of the standard imbed-ding Lie algebra of a Lie triple system and compute the 3-derivations and 3-automorphisms of some 3-dimensional Lie algebra.In Chapter 1,we introduce the background and its recent development and analyzes the motivations and the main results of this thesis.In Chapter 2,we recall some basic definitions and results concerning Lie algebras,3-derivations and 3-automorphisms.In Chapter 3,we use the method of differential and exponential map to show that the 3-derivation Lie algebra of a Lie algebra is the Lie algebra of the 3-automorphism Lie group of the Lie algebra.We establish the explicit relation between 3-derivations and 3-automorphisms of a Lie algebra.In Chapter 4,we study the derivations and automorphisms of the stan-dard imbedding Lie algebra of a Lie triple system.In Chapter 5,we compute the 3-derivations and 3-automorphisms of some 3-dimensional Lie algebra.