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

Author： Nauryzbaev Ruslan  

Publisher： Taylor & Francis Ltd

E-ISSN： 1532-4125|43|5|1791-1801

ISSN： 0092-7872

Source： Communications in Algebra, Vol.43, Iss.5, 2015-05, pp. : 1791-1801

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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.

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