{
  "abstract": "For any finite-dimensional quasi-Hopf algebra $A$, we define the notion of a stable twist of $A$. We show that stable twists form a strict 2-group $\\2ust(A)$, which is equivalent to $\\OAut(\\C{A})^{\\rev}$. Given a group homomorphism $ρ: G \\to \\ost(A)$, we determine the obstruction in $H^3(G,Z_G(A))$ to lift $ρ$ to a $G$-action on $\\C{A}$. We also establish a bijection between such liftings and cocentral cleft extensions of $\\k[G]$ by $A$. The main application of $\\2ust(A)$ is the computation of $\\OAut(\\C{A})$, together with an explicit description of the corresponding tensor autoequivalences. We apply this framework to pointed Hopf algebras $A$ that arise as central extensions of Taft algebras by cyclic groups, and we explicitly determine all of their tensor autoequivalences. The equivariantizations of $\\C{A}$ by $\\ost(A)$ produce a new family of Hopf algebras $\\N(n,ξ)$ of dimension $2nm$, where $ξ$ is a scalar of order $m\\mid n$ such that neither $\\N(n,ξ)$ nor its dual has the Chevalley property. In dimension 24, we prove that $\\N(6,-1)$ and its dual are precisely the Hopf algebras $H$ for which neither $H$ nor $H^*$ has the Chevalley property. This completes the classification of nonsemisimple Hopf algebras of dimension 24.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40228",
  "author_total": 2,
  "authors": [
    {
      "name": "Siu-Hung Ng"
    },
    {
      "name": "Xingting Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/apg2agcm1d49x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40228",
  "fulltext_url": null,
  "id": "apg2agcm1d49x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40228",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40228",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/apg2agcm1d49x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40228",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40228"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On stable twist 2-groups of quasi-Hopf algebras",
  "title_text": "On stable twist 2-groups of quasi-Hopf algebras",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/apg2agcm1d49x",
  "venue": "arXiv",
  "versions": []
}