{
  "abstract": "For an action of an inverse semigroup $S$ on a locally compact Hausdorff space $X$, we construct an étale groupoid $S\\ltimes X^\\mathrm{KS}$, called the KS-groupoid associated with the action. This construction may be viewed as a dynamical analogue of the construction of universal groupoids for inverse semigroups. We provide a dynamical version of Paterson's theorem which states that the full and reduced crossed products (in the sense of Khoshkam and Skandalis) of $C_0(X)$ are canonically isomorphic to the full and reduced groupoid C*-algebras of $S\\ltimes X^\\mathrm{KS}$, respectively. We further investigate some topological properties, functoriality and universality of KS-groupoids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06447",
  "author_total": 1,
  "authors": [
    {
      "name": "Hikaru Sekiyama"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/deaqagvv6r3mp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06447",
  "fulltext_url": null,
  "id": "deaqagvv6r3mp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06447",
  "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.GR"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7212023136",
  "pdf_url": "https://arxiv.org/pdf/2609.06447",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/deaqagvv6r3mp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06447",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06447"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions",
  "title_text": "KS-Groupoids and KS-Crossed Products associated with Inverse Semigroup Actions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/deaqagvv6r3mp",
  "venue": "arXiv",
  "versions": []
}