{
  "abstract": "We give an explicit example of a $W^{*}$-bundle $M$ over a compact, metrizable space $K$, which has each fiber $M_{p}$ a $\\textrm{II}_{1}$-factor with separable predual, and which satisfies the following negation of the generator problem: given any finite family $a_{1},\\cdots,a_{n}\\in M$ of continuous sections, there is a $p\\in K$ (depending upon that family) so that $a_{1,p},\\cdots,a_{n,p}$ do not generate $M_{p}$ as a von Neumann algebra. More generally, if $N$ is a sub-bundle of $M$ with the property that each fiber is hyperfinite, or has a Cartan, or is generated by two commuting diffuse subalgebras, or has diffuse central sequence algebra, or is generated by a single sequential commutation orbit, then given any finite family $a_{1},\\cdots,a_{n}\\in M$ of continuous sections, there is a $p\\in K$ (depending upon that family) so that $a_{1,p},\\cdots,a_{n,p}$ together with $N_{p}$ do not generate $M_{p}$. We discuss implications for the generator problem for von Neumann algebras: e.g. there is no ``continuous\" way to take countably many generators for a tracial von Neumann algebra with separable predual and produce a single generator, at least if such a procedure works for all von Neumann algebras simultaneously.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16428",
  "author_total": 1,
  "authors": [
    {
      "name": "Ben Hayes"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8wx9q3qm4n2jk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16428",
  "fulltext_url": null,
  "id": "8wx9q3qm4n2jk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16428",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213395676",
  "pdf_url": "https://arxiv.org/pdf/2609.16428",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8wx9q3qm4n2jk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.16428",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16428"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "On Generators for $W^{*}$-bundles",
  "title_text": "On Generators for W^*-bundles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/8wx9q3qm4n2jk",
  "venue": "arXiv",
  "versions": []
}