Automorphisms of free metabelian Lie algebras

Abstract

We give a sharpening of a result of Bryant and Drensky [R. M. Bryant and V. Drensky, Dense subgroups of the automorphism groups of free algebras, Canad. J. Math. 45(6) (1993) 1135–1154] for the automorphism group [Formula: see text] of a free metabelian Lie algebra [Formula: see text], with [Formula: see text]. In particular, we prove that the subgroup of [Formula: see text] generated by [Formula: see text] and two more IA-automorphisms is dense in [Formula: see text] and, for [Formula: see text], the subgroup generated by [Formula: see text] and one more IA-automorphism is dense in [Formula: see text].