{
  "abstract": "The Menichetti-Kaplansky theorem states that a finite semifield that is three-dimensional over its center is either a field or a twisted field of Albert. This implies that a quadratic homogeneous bijection of $\\mathbb{P}^2(\\mathbb{F}_q)$ is equivalent to a Dembowski-Ostrom monomial. In this paper, we give a large class of semiquadratic homogeneous bijections of $\\mathbb{P}^2(\\mathbb{F}_q)$ that are inequivalent to Dembowski-Ostrom monomials. Using these bijections, we construct a large family of commutative semifields that are non-isotopic to finite fields or twisted fields, which in turn give rise to a large family of non-Desarguesian commutative semifield planes. Semiquadratic homogeneous bijections of $\\mathbb{P}^1(\\mathbb{F}_q)$ have been classified only recently by the first-named author, and Ding and Zieve with the result that all such bijections are either equivalent to Dembowski-Ostrom monomials or degenerate. We demonstrate that this is not the case for $\\mathbb{P}^2(\\mathbb{F}_q)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.14009",
  "author_total": 2,
  "authors": [
    {
      "name": "Faruk Göloğlu"
    },
    {
      "name": "Lukas Kölsch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/40m2dm7r9cz6r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.14009",
  "fulltext_url": null,
  "id": "40m2dm7r9cz6r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.14009",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7161259579",
  "pdf_url": "https://arxiv.org/pdf/2605.14009",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/40m2dm7r9cz6r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2605.14009",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.14009"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Commutative Semifields from bijections of the Desarguesian plane",
  "title_text": "Commutative Semifields from bijections of the Desarguesian plane",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/40m2dm7r9cz6r",
  "venue": "arXiv",
  "versions": []
}