{
  "id": "2107.03650",
  "version": "v1",
  "published": "2021-07-08T07:34:18.000Z",
  "updated": "2021-07-08T07:34:18.000Z",
  "title": "Inclusions of C*-algebras of graded groupoids",
  "authors": [
    "Becky Armstrong",
    "Lisa Orloff Clark",
    "Astrid an Huef"
  ],
  "comment": "12 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "We consider a locally compact Hausdorff groupoid $G$ which is graded over a discrete group. Then the fibre over the identity is an open and closed subgroupoid $G_e$. We show that the full C*-algebra of this subgroupoid embeds isometrically into the full C*-algebra of the groupoid; this extends a theorem of Kaliszewski--Quigg--Raeburn from the \\'etale to the non-\\'etale setting. We use the same ideas to investigate a possible embedding of the reduced C*-algebra of the subgroupoid in the reduced C*-algebra of the groupoid, and find that there is an obstruction in the kernel of the quotient map from the full to the reduced C*-algebras of $G_e$. As an application we show that the full and reduced C*-algebras of $G$ are topologically graded in the sense of Exel, and we discuss the full and reduced C*-algebras of the associated bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-08T07:34:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05"
    ],
    "keywords": [
      "graded groupoids",
      "inclusions",
      "locally compact hausdorff groupoid",
      "discrete group",
      "subgroupoid embeds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}