{
  "abstract": "Automorphism groups are among the most natural structural invariants of an algebra, and their explicit determination is a basic problem in the structure theory of Leibniz algebras. In a series of earlier papers, automorphism groups were obtained for several classes of low-dimensional, one-generated, nilpotent, and non-nilpotent Leibniz algebras. In the present paper we complete this picture for three-dimensional non-Lie left Leibniz algebras over arbitrary fields. We use a refined organization of the three-dimensional classification into sixteen isomorphism types, including parameterized families. Previously known cases are not recomputed; instead, they are incorporated by reference, with changes of basis recorded when necessary. For the remaining types we determine the automorphism groups explicitly through a direct analysis of the automorphism conditions. Particular attention is paid to exceptional parameter values and to characteristic two. A final table summarizes the automorphism group of every type in the classification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24320",
  "author_total": 3,
  "authors": [
    {
      "name": "Leonid A. Kurdachenko"
    },
    {
      "name": "Oleksandr O. Pypka"
    },
    {
      "name": "Mykola M. Semko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/anbsg8s93h3c8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24320",
  "fulltext_url": null,
  "id": "anbsg8s93h3c8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24320",
  "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": "W7214006569",
  "pdf_url": "https://arxiv.org/pdf/2609.24320",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/anbsg8s93h3c8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.24320",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24320"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Automorphism Groups of Three-Dimensional Leibniz Algebras: A Complete Description",
  "title_text": "Automorphism Groups of Three-Dimensional Leibniz Algebras: A Complete Description",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/anbsg8s93h3c8",
  "venue": "arXiv",
  "versions": []
}