2-local Automorphisms On Basic Classical Simple Lie Superalgebras

The derivations and automorphisms are one of the main research branches of Lie superal-gebras.In this paper,we mainly studied the relationship between 2-local automorphisms and automorphisms on Lie superalgebras over the complex number field.In recent years,the study of 2-local derivation and 2-local automorphism on von Neumann algebras has made a great progress.Recently,some scholars have studied 2-local derivations and 2-local automorphisms of Lie algebra.Because the even part of a Lie superalgebra is a Lie algebra,we would like to study the 2-local derivations and 2-local automorphisms of Lie super algebras.In this article,according to the non-degenerate even invariant bilinear form and root space decomposition,we prove that every 2-local automorphism is an automorphism on basic classical Lie superalgebras over the complex number field whose Killing form is non-degenerate.When Killing form is degenerate,every 2-local automorphism of D(n + 1,n)and A(n,n)(n ? 1)is an automorphism.Furthermore,we give an subalgebra of A(2,2)whose 2-local automorphism is not always an automorphism.So we showed that the 2-local automorphism is not equivalent to the automorphism on all Lie super algebras.