{
  "abstract": "Let \\(G\\) be a finite non-abelian group, let \\(Φ\\in Z^3(G,\\mathbb C^\\times)\\) be normalized, and let \\(V,W\\) be finite-dimensional simple objects of \\({}_G^G\\mathcal{YD}^Φ\\). We classify, up to interchange, the braided-indecomposable pairs \\((V,W)\\) whose supports generate \\(G\\) and for which \\(\\mathcal B(V\\oplus W)\\) is finite-dimensional. The classification consists of eight cases with five possible support quandles. In every case the Cartan graph is standard of type \\(A_2\\), \\(B_2\\), or \\(G_2\\), and the dimension is determined explicitly. A new phenomenon occurs {in the \\(Γ_2\\) case}: the twisted setting admits a family of type \\(G_2\\) absent from the ordinary \\(Γ_2\\) classification and we construct an explicit example over a non-abelian group of order \\(16\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09812",
  "author_total": 1,
  "authors": [
    {
      "name": "Bowen Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/byx41drca11nm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09812",
  "fulltext_url": null,
  "id": "byx41drca11nm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09812",
  "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": "W7212128014",
  "pdf_url": "https://arxiv.org/pdf/2609.09812",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/byx41drca11nm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2609.09812",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09812"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Classification of finite-dimensional Nichols algebras of rank two in twisted Yetter--Drinfeld categories",
  "title_text": "Classification of finite-dimensional Nichols algebras of rank two in twisted Yetter--Drinfeld categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/byx41drca11nm",
  "venue": "arXiv",
  "versions": []
}