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

C. E. Kofinas; A. I. Papistas

paper

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

arXiv:2212.05957

Abstract

For a positive integer $n$ , with $n \geq 4$ , let $R_{n}$ 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 Aut $(R_{n})$ generated by the tame automorphisms and a countably infinite set of explicitly given automorphisms of $R_{n}$ is dense in Aut $(R_{n})$ with respect to the formal power series topology.