{
  "abstract": "We exhibit nonamenable groups whose reduced group C*-algebras are not pure. More precisely, if $Γ$ is any countably infinite discrete group, then the reduced group C*-algebra of the restricted wreath product $(\\mathbb{Z}/2\\mathbb{Z}) \\wr Γ$ has an ideal-quotient isomorphic to $\\mathcal{K}(\\ell^2(Γ))$. It therefore fails to be nowhere scattered and, in particular, is not pure. Taking $Γ$ to be any nonamenable group, we thereby obtain a negative answer to a question of Thiel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10653",
  "author_total": 1,
  "authors": [
    {
      "name": "Jamie Bell"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0shh66sg5s53p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10653",
  "fulltext_url": null,
  "id": "0shh66sg5s53p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10653",
  "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": "W7212311465",
  "pdf_url": "https://arxiv.org/pdf/2609.10653",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0shh66sg5s53p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.10653",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10653"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Nonamenable groups whose reduced group C*-algebras are not pure",
  "title_text": "Nonamenable groups whose reduced group C*-algebras are not pure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/0shh66sg5s53p",
  "venue": "arXiv",
  "versions": []
}