A New Class Of High-dimensional Rds Type Lie Algebra Structure

The structure and classification of Lie algebra is discussed by looking into the lattice of its ideals, which is very interesting and helpful work. RDS type Lie algebras are defined by studying the lattice of its ideals. RDS type Lie Algebra is a special class of Lie Algebra. We define it through studying its ideal lattice. This class of Lie algebras is more than the semi-simple Lie algebra so it can help us to accelerate the whole Lie algebras.This paper is divided into four chapters.The first chapter Some properties of n-RDS type Lie algebras are obtained and a series of results are obtained when the base field is characteristic zero and algebraically closed. Particularly, in the case of n=2 all the n-RDS type Lie algebras are constructed.The second chapter We give some properties of RDS type Lie algebras. The existence theorem of solvable RDS type Lie algebras is presented.The third chapter The structure and classification of Lie algebras whose dimensional is lower or equal to four. we give the amendment of results about four dimensional solvable RDS type Lie algebras and study the five dimensional unsolvable Lie algebras whose central dimensional is 1 to determine not RDS type Lie algebra.The forth chapter Depending on characterizing the ideals of Lie Algebra, a new class of RDS type Lie algebra is constructed.The main work of this paper is to study of RDS type Lie Algebras. This paper is above three chapters, depending on characterizing the ideals of Lie Algebra, a new class of RDS type Lie algebra is constructed, and establish the foundation for studying the high dimensional RDS type Lie algebra.