{
  "abstract": "We determine the Grothendieck rings of fusion categories over $\\mathcal{C}$ containing a nonpointed Tambara--Yamagami fusion subcategory and exactly one further simple object. The subcategory necessarily has rank five, its invertible objects form the Klein four-group, and the coefficient $κ$ of the additional simple object in its tensor square belongs to $\\{0,2,7\\}$. Each of these three based rings is categorifiable. For $κ=0$, every category belongs, up to tensor equivalence, to the rank-one odd-component extension list of Choi--Lu--Sun. For $κ=2$ we construct an explicit unitary group-theoretical realization, and for $κ=7$ a realization is $\\rm{Rep}(\\rm{PSU}(3,2))$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35574",
  "author_total": 3,
  "authors": [
    {
      "name": "Jingcheng Dong"
    },
    {
      "name": "Sébastien Palcoux"
    },
    {
      "name": "Kai Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1v35mbdv2tkg3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35574",
  "fulltext_url": null,
  "id": "1v35mbdv2tkg3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35574",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223790231",
  "pdf_url": "https://arxiv.org/pdf/2610.35574",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1v35mbdv2tkg3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.35574",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35574"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Grothendieck rings of near-Tambara--Yamagami fusion categories",
  "title_text": "Grothendieck rings of near-Tambara--Yamagami fusion categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/1v35mbdv2tkg3",
  "venue": "arXiv",
  "versions": []
}