{
  "abstract": "We classify the Hom--Lie structures on finite-dimensional simple Lie algebras over an algebraically closed field of characteristic different from \\(2\\) and \\(3\\). Except for the three-dimensional simple Lie algebra and the Zassenhaus algebras, every such structure is a scalar multiple of the identity. In the two exceptional cases, we determine the full Hom--Lie space: it has dimension six for the three-dimensional algebra, while for a Zassenhaus algebra it consists precisely of the multiplication operators arising from the corresponding divided-power algebra. This proves a conjecture of Makhlouf and Zusmanovich.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25056",
  "author_total": 3,
  "authors": [
    {
      "name": "Jiacheng Sun"
    },
    {
      "name": "Chi Zhang"
    },
    {
      "name": "Haoran Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a19bha0bmanvb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25056",
  "fulltext_url": null,
  "id": "a19bha0bmanvb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25056",
  "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.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7223021080",
  "pdf_url": "https://arxiv.org/pdf/2610.25056",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a19bha0bmanvb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25056",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25056"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of Hom--Lie structures on finite-dimensional simple Lie algebras",
  "title_text": "Classification of Hom--Lie structures on finite-dimensional simple Lie algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/a19bha0bmanvb",
  "venue": "arXiv",
  "versions": []
}