Automorphisms of Relatively Free Nilpotent Lie Algebras |
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Authors: | Constantinos E Kofinas |
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Institution: | Department of Mathematics, Faculty of Sciences , Aristotle University of Thessaloniki , Thessaloniki, Greece |
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Abstract: | Let L be a relatively free nilpotent Lie algebra over ? of rank n and class c, with n ≥ 2; freely generated by a set 𝒵. Give L the structure of a group, denoted by R, by means of the Baker–Campbell–Hausdorff formula. Let G be the subgroup of R generated by the set 𝒵 and N Aut(L)(G) the normalizer in Aut(L) of the set G. We prove that the automorphism group of L is generated by GL n (?) and N Aut(L)(G). Let H be a subgroup of finite index in Aut(G) generated by the tame automorphisms and a finite subset X of IA-automorphisms with cardinal s. We construct a set Y consisting of s + 1 IA-automorphisms of L such that Aut(L) is generated by GL n (?) and Y. We apply this particular method to construct generating sets for the automorphism groups of certain relatively free nilpotent Lie algebras. |
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Keywords: | Automorphisms Nilpotent Lie algebras Torsion-free nilpotent groups Varieties of Lie algebras |
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