关于李三系的导子和自同构

On Derivation and Automorphism of Lie Triple System

在李三系导子已有性质的基础上,研究了李三系的导子、自同构,以及它们与相应的标准嵌入李代数的导子、自同构间的关系,特别得到了有关内导子和内自同构的一些结论.

Lie triple system,which is a very oimportant algebra system,is introduced in connection.with the symmetric space and the totally geodesic submanifold.Lie triple system connects with many other algebra systems,especially with Lie algebra.Let T be a Lietriple system and L(T) standard imbedding Lie algebra of T.This paper,which bases on some properties of the derivations,will give the definition of natual extension D of the derivation D to L(T),and the definition of natual extension σ of the automorphism σ to L(T),kand will give some relationship on derivations and automorphisms between T and L(T).