On Local Automorphisms of sl2

Abstract

We establish that the set of local automorphisms LAut(sl 2 ) is the group Aut ± (sl 2 ) of all automorphisms and anti-automorphisms. For n ≥ 3 we prove that anti-automorphisms are local automorphisms of sln.

Local and 2-Local Derivations of p-Filiform Leibniz Algebras

“…Local automorphisms of certain finitedimensional simple Lie and Leibniz algebras are investigated in [8]. Concerning local automorphism, T.Becker, J.Escobar, C.Salas and R.Turdibaev in [13] established that the set of local automorphisms LAut(sl 2 ) coincides with the group Aut ± (sl 2 ) of all automorphisms and anti-automorphisms. Later in [15] M.Costantini proved that a linear map on a simple Lie algebra is a local automorphism if and only if it is either an automorphism or an anti-automorphism.…”