On Perfect Lie Triple Systems

Lie triple system is a special generalization of Lie algebra. In general, Lie triple sys-tems have natural embeddings into certain canonical Lie algebras, the so-called standard and universal embeddings.In this thesis, the concept of the perfect Lie triple system is introduced, which is a natural generalization of the concept of perfect Lie algebra. And then, some properties of perfect Lie triple systems are investigated. We prove that the derivation algebra, holomorph, and standard embedding algebra of a centerless perfect Lie triple system over an algebraically closed field K, is complete. And then, the necessary and sufficient condition for the perfect Lie triple system is, the standard embedding algebra is perfect.At last, some properties of perfect restricted Lie triple systems are given, for exam-ple, the ascending and desending central series and so on. We obtain the necessary and sufficient condition for the perfect Lie triple system T is restrictable.