2-Local Derivations,Local Derivations,2-Local Automorphisms And Local Automorphisms On Witt Algebras

Derivation and automorphism are important concepts in algebra.In algebraic the-ory,derivations must be local derivations and 2-local derivations,but local derivations and 2-local derivations are not necessarily derivations;similarly,automorphisms must be local automorphisms and 2-local automorphisms,and local automorphisms and 2-local automorphisms are not necessarily automorphisms.Witt algebras are a very important class of infinite-dimensional Lie algebras,which have many applications in physics and other fields,so it is very meaningful to study properties of Witt algebras.We obtain some results around this issue.Let F be a field of characteristic 0.The vector fields(?),where t₁,t₂,···,t_n are independent variables,and the f_i are Laurent polynomials int₁,t₂,···,t_n form a Lie algebra under the usual bracket operation.This thesis mainly studies a class of infinite dimensional Lie algebras??Witt alge-bras,we study the 2-local derivations,local derivations,2-local automorphisms,and local automorphisms on the algebras,and obtain the following results:(1)2-local derivations on Witt algebras are derivations;(2)local derivations on Witt algebras are derivations;(3)2-local automorphisms on Witt algebras are automorphisms;(4)local automorphisms on Witt algebras are automorphisms.