{
  "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 $n\\geq 5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21954",
  "author_total": 1,
  "authors": [
    {
      "name": "Ualbai Umirbaev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7jsjcgrn58p9j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21954",
  "fulltext_url": null,
  "id": "7jsjcgrn58p9j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21954",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7222745412",
  "pdf_url": "https://arxiv.org/pdf/2610.21954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7jsjcgrn58p9j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphisms of Free Metabelian Lie Algebras, II",
  "title_text": "Automorphisms of Free Metabelian Lie Algebras, II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/7jsjcgrn58p9j",
  "venue": "arXiv",
  "versions": []
}