{
  "abstract": "In this paper, we prove that every super McDuff $\\rm II_1$ factor is uniformly super McDuff. In particular, the classes of super McDuff and uniformly super McDuff $\\rm II_1$ factors coincide. This answers \\cite[Question D]{GJKEP} affirmatively. For factors with separable predual, super McDuffness is therefore equivalent to the Brown property and is preserved under elementary equivalence, also answering \\cite[Question~6.2.1]{AGK22} affirmatively. We further show that every infinite tensor product of non-$Γ$ $\\mathrm{II}_1$ factors is uniformly super McDuff. For a finite tensor product of separable $\\mathrm{II}_1$ factors that is super McDuff, each tensor factor is either non-$Γ$ or uniformly super McDuff, and at least one is uniformly super McDuff.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04842",
  "author_total": 3,
  "authors": [
    {
      "name": "Xinyan Cao"
    },
    {
      "name": "Zhaolin Yao"
    },
    {
      "name": "Xiaoyan Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b7qfep8f4717t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04842",
  "fulltext_url": null,
  "id": "b7qfep8f4717t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04842",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04842",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b7qfep8f4717t.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04842",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04842"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Super McDuff and Uniformly Super McDuff $\\rm II_1$ factor",
  "title_text": "Super McDuff and Uniformly Super McDuff II_1 factor",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/b7qfep8f4717t",
  "venue": "arXiv",
  "versions": []
}