On automorphisms of certain free nilpotent-by-abelian Lie algebras

Abstract

For a positive integer [Formula: see text], let [Formula: see text] be a free (nilpotent of class 2)-by-abelian and abelian-by-(nilpotent of class 2) Lie algebra of rank n. We show that the subgroup of [Formula: see text] generated by the tame automorphisms and a countably infinite set of explicitly given automorphisms of [Formula: see text] is dense in [Formula: see text] with respect to the formal power series topology.