{
  "abstract": "Building on OpenAI's proof of isomorphism of free group factors, we give a self-contained proof of a corresponding result for $C^{*}$-algebras generated by free semicircular systems: the isomorphism class of a $C^{*}$-algebra generated by a semicircular $n$-tuple does not depend on $n\\in\\{2,3,\\dots,+\\infty\\}$. Similarly, reduced free products of $n$ copies of the Jiang--Su algebra are isomorphic for different $n$ in this range. While reduced free group $C^{*}$-algebras of different ranks are not isomorphic (by a result of Pimsner--Voiculescu), we show that they have strong free absorption properties. At the heart of the proof is an automorphism approximation property for inclusions of $C^{*}$- and $W^{*}$-algebras; a relative version of that property was previously used to derive free complementation results.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19590",
  "author_total": 1,
  "authors": [
    {
      "name": "D. Shlyakhtenko"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/featm982y5t13.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19590",
  "fulltext_url": null,
  "id": "featm982y5t13",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19590",
  "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.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7222342787",
  "pdf_url": "https://arxiv.org/pdf/2610.19590",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/featm982y5t13.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.19590",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19590"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "On the Isomorphism of Semicircular Algebras",
  "title_text": "On the Isomorphism of Semicircular Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/featm982y5t13",
  "venue": "arXiv",
  "versions": []
}