Year: 2026
Type: preprint
Abstract: We show that every automorphism of the free metabelian Lie algebra $M_n$ of rank $n\geq 4$ over an arbitrary field $K$ is almost tame; that is, it can be expressed as a product of Chein automorphisms (also called one-row transformations). Moreover, we prove that, for $n\geq 4$, the group $\mathrm{Aut}(M_n)$ of all automorphisms of the free metabelian Lie algebra $M_n$ over a field $K$ of characteristic not equal to $3$ is generated by its linear automorphisms, together with a single quadratic and a single cubic automorphism. The same result holds for fields of any characteristic if $n\geq 5$.
Source: arXiv (Cornell University)
Author: Umirbaev, Ualbai
Institution: Wayne State University
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222745412