Inner and Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

Abstract

Let L m, c be the free metabelian nilpotent of class c Lie algebra of rank m over a field K of characteristic 0. We describe the groups of inner and outer automorphisms of L m, c . To obtain this result, we first describe the groups of inner and continuous outer automorphisms of the completion with respect to the formal power series topology of the free metabelian Lie algebra F m of rank m.