The Automorphism Of Classical Lie Superalgebras

In this paper, we introduce classical Lie superalgebras. By calculating on all kinds of classical Lie superalgebras. we study the existence problem of automorphism, which can leave Cartan subalgebras invariant, send root vectors to its negative, we find that, except P(n), each of them have this automorphism. Especially, we need a lot of calculation to construct the automorphism for D(2,1;α), G(3) and F(4).