{
  "abstract": "We prove a noncommutative topological factor theorem for irreducible lattices in products of real rank-one simple Lie groups. The intermediate C*-subalgebras between the reduced group C*-algebra and the boundary crossed product are exactly the crossed products arising from coordinate subproducts of the Furstenberg boundary. This follows from a more general theorem for product boundary actions, which also yields tree and mixed local-field versions. We finally show that, for lattices in connected semisimple real Lie groups with finite center and no compact factors, the scalar-expectation case of the corresponding classification is equivalent to ordinary ITAP.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07421",
  "author_total": 2,
  "authors": [
    {
      "name": "Cyril Houdayer"
    },
    {
      "name": "Corentin Le Bars"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dbcs1dh0w55k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07421",
  "fulltext_url": null,
  "id": "1dbcs1dh0w55k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07421",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7202149884",
  "pdf_url": "https://arxiv.org/pdf/2608.07421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dbcs1dh0w55k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2608.07421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07421"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The noncommutative topological factor theorem for rank-one product lattices",
  "title_text": "The noncommutative topological factor theorem for rank-one product lattices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/1dbcs1dh0w55k",
  "venue": "arXiv",
  "versions": []
}