{
  "abstract": "As a generalization of Gabe and Neagu's inclusions of real rank zero, we introduce a notion of Property (SP) for inclusions of C*-algebras. We begin the systematic study of SP-inclusions, establishing a topological description in the commutative setting and permanence under many constructions. We also extend known results about the permanence of Property (SP) for C*-algebras under classical symmetries to the setting of quantum symmetries; we show that Property (SP) for (simple, separable) C*-algebras is preserved under irreducible C*-discrete inclusions. Finally, we resolve (in the negative) a question raised by Gabe and Neagu about inclusions coming from Furstenburg boundaries. Namely, we show the existence of a countable, discrete, non-amenable group $G$ such that $C_r^*(G) \\subseteq C(\\partial_F G) \\rtimes_r G$ is not an SP-inclusion (and therefore not an inclusion of real rank zero).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30057",
  "author_total": 2,
  "authors": [
    {
      "name": "Alec Gow"
    },
    {
      "name": "Roberto Hernández Palomares"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e7hydb1nv4yaq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30057",
  "fulltext_url": null,
  "id": "e7hydb1nv4yaq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30057",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7204864619",
  "pdf_url": "https://arxiv.org/pdf/2608.30057",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e7hydb1nv4yaq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30057",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30057"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Property (SP) and Inclusions of C*-algebras",
  "title_text": "Property (SP) and Inclusions of C*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/e7hydb1nv4yaq",
  "venue": "arXiv",
  "versions": []
}