2-local Derivations Of Some Infinite-dimensional Lie Algebras

In this paper,related conclusions of Lie algebras,simple Lie algebras and root space decompositions are recalled,and the basic concepts of derivations and 2-local derivations are introduced.We mainly study whether 2-local derivations on Virasoro algebras,generalized Loop-Witt algebras and infinite-dimensional complete Lie algebras are derivations by extending the one-dimensional homogeneous derivations of Loop algebras over simple Lie algebras.According to the specific form of its derivations,every 2-local derivation on Virasoro algebra is a derivation.The concept of2-local homogeneous derivations is given.It is proved that all 2-local homogeneous derivations on generalized Loop-Witt algebras and infinite-dimensional complete Lie algebras are derivations.This paper is divided into six chapters.In the first chapter,the research background of this paper is given,the corresponding state is introduced,the development trend and also the research significance of the problem is involved in this paper.In the second chapter,relevant prior knowledge of Lie algebras,simple Lie algebras and its derivations are recalled.In the third chapter,the basic definitions and its derivations of Virasoro algebras are introduced and it is obtained that 2-local derivations of Virasoro are derivations.In the fourth chapter,according to the basic concept of generalized Loop-Witt algebras and the specific form of derivations,2-local homogeneous derivations of generalized Loop-Witt algebras is proved to be derivations.In the fifth chapter,using the triangle decomposition and the property of the basis of simple Lie algebras,we certify that 2-local derivations of (?) are derivations by using the definition of 2-local homogeneous derivations.In the last chapter,the main content of this paper is summarized.