A Study On The Lie - Algebra And Its Derivatives

This paper will study the graded Lie algebra and its some properties derivation. Based on the derivation and graded ideal of graded lie algebra,we can deduce the definition of graded derivation ideal and its relevant properties.On this basis,,in order to the substructure of a graded lie algebra have more profound understanding.In the first chapter of this paper mainly introduces the properties of derivation and the definition of graded ideal of graded lie algebra.Thus we can deduce the characteristics of the graded derivation ideal. The second chapter mainly discusses the solvability and nilpotent of the graded algebra. In the third chapter we have reach the concept of semisimple graded lie algebra and graded derivation single algebras, and on this basis, discussed their characteristics of guide. On the basis of the concepts,their characteristics are discussed in this chapter.