On Generators of the Tame Automorphism Group of Free Metabelian Lie Algebras

R. Zh. Nauryzbaev

2015

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DOI 10.1080/00927872.2013.876038
Data confidence 70 medium
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Abstract

We prove that the tame automorphism group TAut(M n ) of a free metabelian Lie algebra M n in n variables over a field k is generated by a single nonlinear automorphism modulo all linear automorphisms if n ≥ 4 except the case when n = 4 and char(k) ≠ 3. If char(k) = 3, then TAut(M 4) is generated by two automorphisms modulo all linear automorphisms. We also prove that the tame automorphism group TAut(M 3) cannot be generated by any finite number of automorphisms modulo all linear automorphisms.