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arXiv · 2406.12884

Automorphisms of free metabelian Lie algebras, I

Ualbai Umirbaev
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Abstract

We show that all Chein automorphisms (or one-row transformations) of lower degree $\geq 4$ of a free metabelian Lie algebra $M_n$ of rank $n\geq 4$ over an arbitrary field $K$ of characteristic $\neq 3$ are tame. We then show that all exponential automorphisms of $M_n$ of lower degree $\geq 5$ are also tame under the same conditions. The same results hold for fields of any characteristic when $n\geq 5$. These results contradict some long-standing results in the area. We also prove that a large class of automorphisms of $M_n$ of rank $n\geq 4$ that move only two variables are almost tame, that is, they can be expressed as a product of Chein automorphisms.

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Ualbai Umirbaev. 2024-05-30. Automorphisms of free metabelian Lie algebras, I. https://arxiv.org/abs/2406.12884

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