On Automorphisms of Free Center-by-Metabelian Lie Algebras

scot william r.;

Let Cn be the free center-by-metabelian Lie algebra of finite rank n, with n ≥ 2, over a field K of characteristic 0.We study the automorphism group Aut(Cn) of Cn by means of a topology. Let TCn
be the group of tame automorphisms of Cn and GLn(K) be the general linear group. It is shown that for any finite subset X of IA-automorphisms of C2, the subgroup of Aut(C2) generated by
GL2(K) and X is not dense in Aut(C2). For n = 3, the subgroup of Aut(C3) generated by TC3 and two more IA-automorphisms is dense in Aut(C3). For n ≥ 4, the subgroup of Aut(Cn) generated by TCn and one more IA-automorphism is dense in Aut(Cn).