{
  "abstract": "We study when a finite-dimensional pre-Nichols algebra $R$ of $V$ over an algebraically closed field of characteristic $p>0$, with $p\\nmid\\dim R$, is necessarily isomorphic to the Nichols algebra $\\B(V)$. A trace identity gives a rigidity criterion involving the twist on minimal defining relations. Using integral forms and Hochschild cohomology, we establish uniform rigidity for Yetter--Drinfeld modules of bounded dimension over fixed finite abelian groups, and obtain related results for certain modules over nonabelian groups. For every finite group $G$ of odd order, outside finitely many characteristics depending only on $G$, every finite-dimensional pointed Hopf algebra $H$ with $G(H)\\simeq G$ and dimension prime to the characteristic is generated by group-like and skew-primitive elements. If $G$ is abelian, then, outside a possibly larger finite set of characteristics, every such $H$ is a Hopf $2$-cocycle deformation of its associated graded Hopf algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25242",
  "author_total": 1,
  "authors": [
    {
      "name": "Rongchuan Xiong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/05vscp078bdyj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25242",
  "fulltext_url": null,
  "id": "05vscp078bdyj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25242",
  "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": "W7223034189",
  "pdf_url": "https://arxiv.org/pdf/2610.25242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/05vscp078bdyj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Pre-Nichols algebras and generation of pointed Hopf algebras in positive characteristic",
  "title_text": "Pre-Nichols algebras and generation of pointed Hopf algebras in positive characteristic",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/05vscp078bdyj",
  "venue": "arXiv",
  "versions": []
}