{
  "abstract": "Let $B_\\infty$ be the braid group on infinitely many strands and $P_\\infty$ its pure braid group. We show that $C^*_r(P_\\infty)\\subseteq C^*_r(B_\\infty)$ and all its intermediate inclusions are $\\mathcal{Z}$-stable and completely selfless. This gives natural examples of simple nonnuclear $\\mathcal{Z}$-stable $C^*$-algebras. Further examples come from $\\mathrm{SL}_\\infty(\\mathbb{Z})$ and $\\mathrm{GL}_\\infty(\\mathbb{Z})$. We also show that $C^*_r(\\mathbb{F}_\\infty)\\subseteq C^*_r(B_\\infty)$ is completely selfless for the free group $\\mathbb{F}_\\infty$ of braids in which only the first strand moves. All results hold for twisted group $C^*$-algebras. In contrast, $\\mathcal{Z}$-stability fails for $B_n$ with $n$ finite and for groups that are not inner amenable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.38596",
  "author_total": 1,
  "authors": [
    {
      "name": "Tron Omland"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6708wp99wjy2k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.38596",
  "fulltext_url": null,
  "id": "6708wp99wjy2k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.38596",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7215108119",
  "pdf_url": "https://arxiv.org/pdf/2609.38596",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6708wp99wjy2k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2609.38596",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.38596"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "$\\mathcal{Z}$-stable and selfless inclusions for the infinite braid group",
  "title_text": "𝒵-stable and selfless inclusions for the infinite braid group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/6708wp99wjy2k",
  "venue": "arXiv",
  "versions": []
}