{
  "abstract": "We introduce NS-Leibniz bialgebras and establish their equivalence with matched pairs and Manin triples of NS-Leibniz algebras. In the coboundary case, skew-symmetric solutions of the NS-Leibniz Yang--Baxter equation yield NS-Leibniz bialgebras and correspond to $\\mathcal{O}$-operators for the dual regular representation. We study quasi-triangular and factorizable structures, and relate factorizable tensors to quadratic Rota--Baxter NS-Leibniz algebras of any fixed nonzero weight. We also construct compatible bialgebra structures from skew-adjoint Nijenhuis operators commuting with the Rota--Baxter operator.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39190",
  "author_total": 2,
  "authors": [
    {
      "name": "Bei Li"
    },
    {
      "name": "Dingguo Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d7zjtx7d45jfk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39190",
  "fulltext_url": null,
  "id": "d7zjtx7d45jfk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39190",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d7zjtx7d45jfk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39190"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators",
  "title_text": "NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/d7zjtx7d45jfk",
  "venue": "arXiv",
  "versions": []
}