{
  "abstract": "We consider an action of an inverse semigroup on a C*-algebra $A$ and use it to construct a groupoid of germs with unit space the spectrum of $A$. Motivated by the representation theory of C*-algebras of groupoids, we construct a concrete family of covariant representations for the action. We use this family to give new definitions of the reduced and essential crossed product C*-algebras that avoid, respectively, passing to the double commutant and local multiplier algebra of $A$. Our reduced crossed product is isomorphic to the one defined by Exel, Buss and Meyer, and when the inverse semigroup is quasi-countable our essential crossed product is isomorphic to the one defined by Kwaśniewski and Meyer.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25694",
  "author_total": 2,
  "authors": [
    {
      "name": "Astrid an Huef"
    },
    {
      "name": "Ilija Tolich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0whd9bpvdj7es.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25694",
  "fulltext_url": null,
  "id": "0whd9bpvdj7es",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25694",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7214114416",
  "pdf_url": "https://arxiv.org/pdf/2609.25694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0whd9bpvdj7es.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Covariant representations of actions of inverse semigroups: a new approach to the reduced and essential crossed-product C*-algebras",
  "title_text": "Covariant representations of actions of inverse semigroups: a new approach to the reduced and essential crossed-product C*-algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/0whd9bpvdj7es",
  "venue": "arXiv",
  "versions": []
}