PreprintCC BY 4.0arXiv
Automorphisms of Free Metabelian Lie Algebras, II
Abstract
We show that every automorphism of the free metabelian Lie algebra Mn of rank n≥ 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≥ 4, the group Aut(Mn) of all automorphisms of the free metabelian Lie algebra Mn 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≥ 5.
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BibTeX
@misc{umirbaev2026automorphisms,
title = {{Automorphisms of Free Metabelian Lie Algebras, II}},
author = {Ualbai Umirbaev},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21954},
eprint = {2610.21954},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21954},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Automorphisms of Free Metabelian Lie Algebras, II
AU - Ualbai Umirbaev
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21954
UR - https://arxiv.org/abs/2610.21954
AB - We show that every automorphism of the free metabelian Lie algebra M_n of rank n≥ 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≥ 4, the group 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≥ 5.
ER -