{
  "abstract": "Burde proved that the Lie algebra $\\mathfrak{sl}_2(\\mathbb{K})$, over a field $\\mathbb{K}$ of characteristic $p > 2$, admits compatible left-symmetric algebra structures if and only if $p = 3$. Since the even part of the Lie superalgebra $\\mathfrak{osp}(1|2)$ is isomorphic to $\\mathfrak{sl}_2(\\mathbb{K})$, we ask whether Burde's structures can be extended to compatible left-symmetric superalgebra structures on $\\mathfrak{osp}(1|2)$. We verify Burde's left-symmetric structures on $\\mathfrak{sl}_2(\\mathbb{K})$, and then test their possible extensions to $\\mathfrak{osp}(1|2)$. We show that no such extension exists in characteristic 3. Together with the obstruction coming from the even part for characteristic $0$ and $p > 3$, this gives non-existence for a field $\\mathbb{K}$ of characteristic different from $2$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12489",
  "author_total": 1,
  "authors": [
    {
      "name": "Josemaria Loza"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94gkyky7s43ak.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12489",
  "fulltext_url": null,
  "id": "94gkyky7s43ak",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12489",
  "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": "W7221503204",
  "pdf_url": "https://arxiv.org/pdf/2610.12489",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94gkyky7s43ak.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12489",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12489"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the non-existence of a left-symmetric structure on osp(1|2) in any characteristic",
  "title_text": "On the non-existence of a left-symmetric structure on osp(1|2) in any characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/94gkyky7s43ak",
  "venue": "arXiv",
  "versions": []
}