{
  "abstract": "We introduce a class of separable II$_1$ factors $M$ admitting no non-trivial crossed product decompositions: $M\\not\\cong B\\rtimes_σG$, for any trace preserving action $G\\curvearrowright^σ(B,τ)$ of an infinite countable group $G$ on a tracial von Neumann algebra $(B,τ)$. These provide the first examples of II$_1$ factors that do not arise as crossed products of noncommutative dynamical systems. Our approach relies on a novel construction of separable II$_1$ factors $M$ whose embeddings into their tensor product square $M\\overline{\\otimes}M$ all arise from the canonical embeddings $x\\mapsto x\\otimes 1$ and $x\\mapsto 1\\otimes x$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.31929",
  "author_total": 3,
  "authors": [
    {
      "name": "Adriana Fernández Quero"
    },
    {
      "name": "Adrian Ioana"
    },
    {
      "name": "Hui Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g11000fn8s3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.31929",
  "fulltext_url": null,
  "id": "4g11000fn8s3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.31929",
  "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.FA"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7166811682",
  "pdf_url": "https://arxiv.org/pdf/2606.31929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g11000fn8s3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2606.31929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.31929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A class of II$_1$ factors without non-trivial crossed product decompositions",
  "title_text": "A class of II_1 factors without non-trivial crossed product decompositions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4g11000fn8s3c",
  "venue": "arXiv",
  "versions": []
}