{
  "abstract": "In this paper, we study the strong irreducibility of a class of operators associated with irrational rotation algebras in the hyperfinite type $\\mathrm{II}_1$ factor $\\mathcal R$. By developing weighted shift models for their relative commutants, we obtain $K_0$ calculations and splitting criteria for direct sums. In particular, we construct strongly irreducible operators in $\\mathcal R$ whose relative commutants have $K_0$-groups isomorphic to $\\mathbb Z$ and $\\mathbb Z^2$. We realize every Jones index of an irreducible subfactor of $\\mathcal R$ as $[\\mathcal R:W^*(T)]$ for some strongly irreducible operator $T$ relative to $\\mathcal R$. Furthermore, we construct strong generators of $\\mathcal R$ and strongly irreducible operators in every type $\\mathrm{II}_1$ factor $\\mathcal M$ with separable predual.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.22028",
  "author_total": 4,
  "authors": [
    {
      "name": "Junsheng Fang"
    },
    {
      "name": "Chunlan Jiang"
    },
    {
      "name": "Minghui Ma"
    },
    {
      "name": "Rui Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agjgpktahgg1x.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.22028",
  "fulltext_url": null,
  "id": "agjgpktahgg1x",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.22028",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222685339",
  "pdf_url": "https://arxiv.org/pdf/2610.22028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/agjgpktahgg1x.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.22028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.22028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Strongly irreducible operators, $K_0$-groups, and Jones indices in the hyperfinite type $\\mathrm{II}_1$ factor",
  "title_text": "Strongly irreducible operators, K_0-groups, and Jones indices in the hyperfinite type II_1 factor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/agjgpktahgg1x",
  "venue": "arXiv",
  "versions": []
}