{
  "abstract": "We characterise C*-irreducible regular C*-inclusions using a number of different conditions considered by different authors. In particular, we show that all C*-irreducible regular inclusions $A\\subseteq B$ are modelled by outer Fell bundles $(B_{g})_{g\\in G}$ over discrete groups with a simple unit fibre $A=B_1$. In this case, we prove a bijection between intermediate C*-algebras $A\\subseteq C \\subseteq B$ and subgroups $H$ of $G$. This extends the Galois correspondence for reduced crossed products by discrete group actions established by Cameron-Smith. We relate it to the Galois correspondences of Izumi and Mukohara for fixed-point algebras of actions of compact abelian groups, and the mixed inclusion of a fixed-point algebra in a reduced crossed product considered by Echterhoff-Rørdam. In addition, using a recent result of Geffen-Ursu, we show that the inclusion of a fixed-point subalgebra $A\\subseteq B$ of an action of $\\mathbb{T}$ or $\\mathbb{Z}/p$ for a square-free number $p>0$ is aperiodic if and only if $A$ detects ideals in $B$. We apply this to give examples of C*-irreducible inclusions coming from Cuntz-Pimsner algebras, including crossed products by endomorphisms or transfer operators. In particular, we characterise when a core subalgebra of a graph C*-algebra is C*-irreducible. Lastly, we show that a general regular topologically graded C*-inclusion $A\\subseteq B$ is aperiodic and has a unique pseudo-expectation provided $A$ detects ideals in all intermediate C*-algebras of $B$. This partially answers a question by Pitts-Zarikian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27518",
  "author_total": 2,
  "authors": [
    {
      "name": "B. K. Kwaśniewski"
    },
    {
      "name": "R. Meyer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1fja2hesbq1cn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27518",
  "fulltext_url": null,
  "id": "1fja2hesbq1cn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27518",
  "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": "W7214209258",
  "pdf_url": "https://arxiv.org/pdf/2609.27518",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1fja2hesbq1cn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27518",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27518"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "C*-irreducible regular inclusions, Galois correspondence and aperiodicity",
  "title_text": "C*-irreducible regular inclusions, Galois correspondence and aperiodicity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/1fja2hesbq1cn",
  "venue": "arXiv",
  "versions": []
}