{
  "abstract": "Let $M$ be the free metabelian Lie algebra of rank $4$ over the field of complex numbers $\\mathbb{C}$. We construct a non-linearizable action of the symmetric group $S_3$, the smallest nonabelian group, on $M$ by automorphisms. We also construct a non-linearizable action of $S_3$ on free metabelian associative algebras of rank $4$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26060",
  "author_total": 2,
  "authors": [
    {
      "name": "Altyngul Naurazbekova"
    },
    {
      "name": "Ualbai Umirbaev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hhfkyb8cqas6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26060",
  "fulltext_url": null,
  "id": "8hhfkyb8cqas6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26060",
  "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": "W7223047011",
  "pdf_url": "https://arxiv.org/pdf/2610.26060",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hhfkyb8cqas6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26060",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26060"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Non-linearizable Action of $S_3$ on Free Metabelian Lie and Associative Algebras",
  "title_text": "A Non-linearizable Action of S_3 on Free Metabelian Lie and Associative Algebras",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/8hhfkyb8cqas6",
  "venue": "arXiv",
  "versions": []
}