{
  "abstract": "Let $K/F$ be a cyclic Galois field extension of degree $n$ with $\\mathrm{Gal}(K/F)=\\langleσ\\rangle$. The nonassociative Petit algebras $K[t;σ]/K[t;σ](t^m-a)$ have recently emerged as important tools in coding theory and cryptography, where the applications only require distinct algebras up to isomorphism. Algebras that are isomorphic via a monomial isomorphism of degree one are called equivalent. We present a novel and precise parametrization of the $F$-equivalence classes of these algebras in the key case that $F$ contains a primitive $n$th root of unity and $n\\mid m$. We evaluate the parametrization explicitly when $F$ is a nonarchimedean local field, which has applications to the number field case recently used to construct a nonassociative variant of Learning with Errors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30921",
  "author_total": 2,
  "authors": [
    {
      "name": "Monica Nevins"
    },
    {
      "name": "Susanne Pumpluen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1kyeh9zp2jqq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30921",
  "fulltext_url": null,
  "id": "c1kyeh9zp2jqq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30921",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7223356849",
  "pdf_url": "https://arxiv.org/pdf/2610.30921",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1kyeh9zp2jqq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.30921",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30921"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A parametrization of nonassociative Petit algebras $K[t;σ]/K[t:σ](t^m-a)$ up to equivalence",
  "title_text": "A parametrization of nonassociative Petit algebras K[t;σ]/K[t:σ](t^m−a) up to equivalence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/c1kyeh9zp2jqq",
  "venue": "arXiv",
  "versions": []
}