{
  "abstract": "In this work, we study restricted Laistrygonian algebras over a field of positive characteristic $p$. We compute their Drinfeld double $\\mathtt{D_p(q,a)}$ and give explicit presentations by generators and relations. We prove that $\\mathtt{D_p(q,a)}$ is a pointed Hopf algebra. For $\\mathtt{D_p(1,a)}$, we describe an abelian exact sequence of Hopf algebras and identify one of its quotients as a restricted enveloping Lie algebra. This exact sequence enables us to classify the finite-dimensional simple $\\mathtt{D_p(1,a)}$-modules. We also introduce an infinite-dimensional Hopf algebra covering the restricted Drinfeld double and study its relation with the corresponding finite-dimensional case. Using this covering together with a Frobenius map, we construct a $3\\times 3$ commutative diagram whose rows and columns are exact sequences of Hopf algebras. In particular, our approach provides a unified treatment of the Drinfeld doubles associated with restricted Laistrygonian algebras in arbitrary positive characteristic.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16665",
  "author_total": 6,
  "authors": [
    {
      "name": "Nicolás Andruskiewitsch"
    },
    {
      "name": "Dirceu Bagio"
    },
    {
      "name": "Saradia Della Flora"
    },
    {
      "name": "Daiana Flores"
    },
    {
      "name": "Oscar Márquez"
    },
    {
      "name": "Héctor Martín Peña Pollastri"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9gdkn0tczn327.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16665",
  "fulltext_url": null,
  "id": "9gdkn0tczn327",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16665",
  "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.QA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221768722",
  "pdf_url": "https://arxiv.org/pdf/2610.16665",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9gdkn0tczn327.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16665",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16665"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Drinfeld doubles of Laistrygonian algebras in positive characteristic",
  "title_text": "On the Drinfeld doubles of Laistrygonian algebras in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/9gdkn0tczn327",
  "venue": "arXiv",
  "versions": []
}