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- W2045887880 abstract "Let |$C_{n}$| be the free center-by-metabelian Lie algebra of finite rank |$n$|, with |$n geq 2$|, over a field |$K$| of characteristic |$0$|. We study the automorphism group |${rm Aut}(C_{n})$| of |$C_{n}$| by means of a topology. Let |$T_{C_{n}}$| be the group of tame automorphisms of |$C_{n}$| and |${rm GL}_{n}(K)$| be the general linear group. It is shown that for any finite subset |$X$| of IA-automorphisms of |$C_{2}$|, the subgroup of |${rm Aut}(C_{2})$| generated by |${rm GL}_{2}(K)$| and |$X$| is not dense in |${rm Aut}(C_{2})$|. For |$n = 3$|, the subgroup of |${rm Aut}(C_{3})$| generated by |$T_{C_{3}}$| and two more IA-automorphisms is dense in |${rm Aut}(C_{3})$|. For |$n geq 4$|, the subgroup of |${rm Aut}(C_{n})$| generated by |$T_{C_{n}}$| and one more IA-automorphism is dense in |${rm Aut}(C_{n})$|." @default.
- W2045887880 created "2016-06-24" @default.
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- W2045887880 date "2015-04-08" @default.
- W2045887880 modified "2023-09-23" @default.
- W2045887880 title "ON AUTOMORPHISMS OF FREE CENTER-BY-METABELIAN LIE ALGEBRAS" @default.
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- W2045887880 doi "https://doi.org/10.1093/qmath/hav008" @default.
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