Automorphisms of free metabelian Lie algebras

We show that every automorphism of a free metabelian Lie algebra Mₙ of rank n≥ 4 over an arbitrary field K is almost tame, that is, it is a product of so-called Chein automorphisms (or one-row transformations). Moreover, we show that the group of all automorphisms Aut(Mₙ) of Mₙ of rank n≥ 4 over a field K of characteristic ≠ 3 is generated by all linear automorphisms, as well as one quadratic and one cubic automorphism. The same result holds for fields of any characteristic if n≥ 5. We also show that all Chein automorphisms of lower degree ≥ 4 and all exponential automorphisms of lower degree ≥ 5 are tame, which contradicts the results of {BN,OE}.