Tame and almost tame automorphisms of free metabelian Lie algebras of rank 3

Altyngul Naurazbekova, B. A. Duisengaliyeva, Ualbai Umirbaev

2026

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DOI 10.1142/s0218196726410134
Data confidence 85 high
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Abstract

In this paper, we show that the group of all tame automorphisms of the free metabelian Lie algebra [Formula: see text] of rank [Formula: see text] over a field is an amalgamated free product of its subgroups. Moreover, we prove that the group of all almost tame automorphisms — that is, the subgroup generated by all Chein automorphisms (or one row transformations) of [Formula: see text] — also admits an amalgamated free product structure. By using these results, we provide simpler proofs of the wildness of certain automorphisms.