Two-Local Superderivations And Two-Local Automorphisms Of Classical Lie Superalgebras

Let F be an algebraically closed field of characteristic zero,and g be any finitedimensional classical Lie superalgebras over F with the non-degenerate Killing form.We prove that every 2-local automorphism on g is an automorphism.We also provide two examples of non-classical Lie superalgebras on which there exists a 2-local automorphism(2-local superderivation)that is not an automorphism(superderivation).