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- Title
ON AUTOMORPHISMS OF FREE CENTER-BY-METABELIAN LIE ALGEBRAS.
- Authors
KOFINAS, C. E.; PAPISTAS, A. I.
- Abstract
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).
- Subjects
AUTOMORPHISMS; LIE algebras; FREE metabelian groups; VECTOR spaces; MATHEMATICAL decomposition
- Publication
Quarterly Journal of Mathematics, 2015, Vol 66, Issue 2, p625
- ISSN
0033-5606
- Publication type
Article
- DOI
10.1093/qmath/hav008