Automorphisms of toroidal Lie superalgebras

We give a description of the algebraic group Aut(g) of automorphisms of a simple finite-dimensional Lie superalgebra g over an algebraically closed field k of characteristic 0, which is obtained by viewing g as a module over a Levi subalgebra of its even part. As an application, we give a detailed description of the group of automorphism of the k-Lie superalgebra g⊗kR for a large class of commutative rings R.