{
  "abstract": "In this paper, we study structural and rigidity properties of $q$-Araki--Woods factors arising from strongly continuous orthogonal representations of $\\R$. We first introduce an AO-type boundary property that is formulated in terms of length projections on the $q$-Fock spaces, and prove that all $q$-Araki--Woods factors satisfy this condition. We next characterize uniform convergence of the associated malleable deformations. We then use these two ingredients as a substitute for weak containment in the coarse bimodule and deduce several rigidity theorems in the framework of Popa's deformation/rigidity theory. As a main consequence, we prove that every $q$-Araki--Woods factor is stably strongly solid. We also prove a normalizer rigidity theorem for inclusions arising from direct sum representations. Finally, we compute Connes' $τ$-invariant, and construct a continuum of pairwise non-isomorphic type $\\mathrm{III}_1$ $q$-Araki--Woods factors with the same $τ$-invariant.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27520",
  "author_total": 1,
  "authors": [
    {
      "name": "Yusuke Isono"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/afeg5bvsaw558.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27520",
  "fulltext_url": null,
  "id": "afeg5bvsaw558",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27520",
  "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": "W7223113973",
  "pdf_url": "https://arxiv.org/pdf/2610.27520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/afeg5bvsaw558.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A boundary approach to rigidity of $q$-Araki--Woods factors",
  "title_text": "A boundary approach to rigidity of q-Araki--Woods factors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/afeg5bvsaw558",
  "venue": "arXiv",
  "versions": []
}