{
  "abstract": "We introduce the notion of Boomerang subalgebras of group von Neumann algebras and study their general properties. We show that every Boomerang subalgebra of $L(Γ)$ is the group von Neumann algebra of a Boomerang subgroup when $Γ$ is a countable $C^*$-simple acylindrically hyperbolic group or a finite product of such groups. Consequently, every such group is invariant random algebra (IRA) rigid: every IRA arises as the pushforward of an invariant random subgroup (IRS) under the group von Neumann algebra construction. We also establish IRA rigidity for adjoint $K$-split higher rank $S$-arithmetic groups, as well as for all countable mixed identity-free (MIF) groups and their finite products. Consequently, IRA rigidity holds for countable groups admitting a topologically free minimal extremely proximal action on a compact Hausdorff space with more than two points. The same conclusion holds for countable groups admitting a faithful minimal action of general type on a tree whose induced boundary action is topologically free, and for finite products of groups admitting either of these actions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41417",
  "author_total": 4,
  "authors": [
    {
      "name": "Tattwamasi Amrutam"
    },
    {
      "name": "Yair Glasner"
    },
    {
      "name": "Yair Hartman"
    },
    {
      "name": "Yongle Jiang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eprdekvfeswqb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41417",
  "fulltext_url": null,
  "id": "eprdekvfeswqb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41417",
  "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.FA"
    ],
    [
      "arxiv",
      "math.GN"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eprdekvfeswqb.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41417"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GN",
      "subfield": "geometry-topology"
    }
  ],
  "title": "IRA Rigidity and boomerang subalgebras of group von Neumann algebras",
  "title_text": "IRA Rigidity and boomerang subalgebras of group von Neumann algebras",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/eprdekvfeswqb",
  "venue": "arXiv",
  "versions": []
}