{
  "abstract": "In this paper, we first construct the dual of a representation of a pre-Leibniz algebra and study infinitesimal deformations of a pre-Leibniz algebra with a representation, which lead to Nijenhuis pairs, characterizing trivial deformations, and to dual-Nijenhuis pairs. Building on these notions, we introduce Kupershmidt-(dual-)Nijenhuis structures and show that they give rise to hierarchies of pairwise compatible Kupershmidt operators, the converse holding under an invertibility condition. Finally, we show that Rota--Baxter--Nijenhuis structures, $r$-$n$ structures and BN-structures all arise as particular cases, and that the first two correspond to each other on quadratic pre-Leibniz algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40837",
  "author_total": 1,
  "authors": [
    {
      "name": "Sami Benabdelhafidh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/esr77fn9j6ev8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40837",
  "fulltext_url": null,
  "id": "esr77fn9j6ev8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40837",
  "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/2610.40837",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/esr77fn9j6ev8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40837",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40837"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Kupershmidt--Nijenhuis structures on pre-Leibniz algebras",
  "title_text": "Kupershmidt--Nijenhuis structures on pre-Leibniz algebras",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/esr77fn9j6ev8",
  "venue": "arXiv",
  "versions": []
}