{
  "abstract": "In this paper, we investigate $\\frac{1}{2}$-derivations and their corresponding local and 2-local analogues on three-dimensional nilpotent Lie--Yamaguti algebras over a field $\\mathbb{F}$ of characteristic zero. Utilizing the established classification of these algebras, we explicitly determine their structures of $\\frac{1}{2}$-derivations and biderivations. Furthermore, we characterize the matrix representations of their local $\\frac{1}{2}$-derivations. Our findings demonstrate that, for the non-abelian algebras under consideration, the space of local $\\frac{1}{2}$-derivations is strictly larger than that of ordinary $\\frac{1}{2}$-derivations. In addition, we construct examples of 2-local $\\frac{1}{2}$-derivations that fail to be global $\\frac{1}{2}$-derivations. Finally, a complete characterization of the biderivations for these algebras is provided.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24852",
  "author_total": 1,
  "authors": [
    {
      "name": "Hassan Oubba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxvcqr2e3jn2h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24852",
  "fulltext_url": null,
  "id": "dxvcqr2e3jn2h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24852",
  "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.AG"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7223012583",
  "pdf_url": "https://arxiv.org/pdf/2610.24852",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxvcqr2e3jn2h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24852",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24852"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "$\\frac{1}{2}$ derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras",
  "title_text": "1/2 derivations and biderivations of 3-dimensional nilpotent Lie-Yamaguti algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/dxvcqr2e3jn2h",
  "venue": "arXiv",
  "versions": []
}