{
  "abstract": "Let $Γ$ be a countable discrete group acting on a tracial von Neumann algebra $(Q,τ_Q)$ in a trace-preserving way. We study invariant von Neumann subalgebras of $Q\\rtimesΓ$ and of $L(Γ)\\bar\\otimes Q$, where the latter is equipped with the diagonal action. We show that, under the pointwise weak mixing assumption, an invariant subalgebra whose image under the canonical conditional expectation onto $Q$ is scalar is necessarily contained in $L(Γ)$. Further, under relative weak mixing and central freeness assumptions, we determine the structure of invariant subalgebras of the crossed product with non-trivial intersection with $Q$. For p.m.p. actions of groups with trivial amenable radical and the invariant subalgebras rigidity property, pointwise relative weak mixing gives a complete classification of invariant subalgebras in the tensor product case. We construct essentially free, prime, pointwise weakly mixing p.m.p. actions of $\\mathbb{F}_n$ for every $2\\leq n\\leq\\infty$, as well as non-prime examples with explicitly described factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19023",
  "author_total": 4,
  "authors": [
    {
      "name": "Tattwamasi Amrutam"
    },
    {
      "name": "Artem Dudko"
    },
    {
      "name": "Yongle Jiang"
    },
    {
      "name": "Adam Skalski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83sv4ash2jxsj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19023",
  "fulltext_url": null,
  "id": "83sv4ash2jxsj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19023",
  "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.DS"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7221952934",
  "pdf_url": "https://arxiv.org/pdf/2610.19023",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83sv4ash2jxsj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19023",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19023"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Invariant von Neumann subalgebras of crossed products and tensor products",
  "title_text": "Invariant von Neumann subalgebras of crossed products and tensor products",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/83sv4ash2jxsj",
  "venue": "arXiv",
  "versions": []
}