A Class Of Lie Algebras With Finite Properties

In the study of Lie algebras,the properties of ideals,subalgebras and maximal ideals of Lie algebras are closely related to their own structures.In this paper,we will focus on two kinds of Lie algebras over the complex field C,namely,Lie algebras with finitely many subalgebras whose dimensions are greater than 1 and Lie algebras with finitely many maximal proper ideals.The first chapter briefly introduces the research background and present situation of Lie algebras,and expounds the main work of this paper.In chapter 2,this paper mainly introduces the definitions and common conclusions in the paper.In chapter 3,we first prove that semisimple Lie algebras over the complex field C do not have subalgebras with finitely many dimensions greater than 1,and then obtain the form of solvable Lie algebras with finitely many dimensions greater than 1.Finally,the form of Lie algebras with finitely many subalgebras whose dimensions greater than 1 over the complex field C is obtained by means of the known classification result and Levi decomposition theorem of the three-dimensional solvable Lie algebras.In chapter 4,we focus on the form of solvable Lie algebras with finitely many maximal proper thoughts over the complex field C.Then,some basic properties of Lie algebras with finitely many maximal proper ideas are provided.In this paper,we study Lie algebras with subalgebras whose finitely many dimensions greater than 1 and Lie algebras with finitely many maximal proper ideas,which enrich the content of the study of Lie algebras and deepen the understanding of special Lie algebras.