{
  "abstract": "We introduce the notion of a Cartan inverse semigroup and an (algebraic) semi-Cartan subalgebra in an $R$-algebra A, providing a purely algebraic analogue of Cartan semigroups and semi-Cartan subalgebras in a C*-algebra. This extends the theory of quasi-Cartan subalgebras, shifting the focus from designated subalgebras to designated subsemigroups. Our main result characterises twisted Steinberg algebras in terms of the existence of a Cartan inverse semigroup: we show that an $R$-algebra admits a Cartan inverse semigroup if and only if it is isomorphic to a twisted Steinberg algebra. Moreover, when our construction is applied to a twisted Steinberg algebra over an ample Hausdorff groupoid, the constructed twist is naturally isomorphic to the original one.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04548",
  "author_total": 4,
  "authors": [
    {
      "name": "Nathan Brownlowe"
    },
    {
      "name": "Lisa Orloff Clark"
    },
    {
      "name": "Ying-Fen Lin"
    },
    {
      "name": "Lynnel D. Naingue"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dzckrjq4serre.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04548",
  "fulltext_url": null,
  "id": "dzckrjq4serre",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04548",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7220736464",
  "pdf_url": "https://arxiv.org/pdf/2610.04548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dzckrjq4serre.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Cartan inverse semigroups and twisted Steinberg algebras",
  "title_text": "Cartan inverse semigroups and twisted Steinberg algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dzckrjq4serre",
  "venue": "arXiv",
  "versions": []
}