Mathematical analysis demonstrates dense automorphism subgroups in free nilpotent-by-abelian Lie algebras, suggesting constructive generation under the formal power series topology.
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.
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Kofinas et al. (2024) studied this question.