{
  "id": "1503.03521",
  "version": "v1",
  "published": "2015-03-11T22:12:01.000Z",
  "updated": "2015-03-11T22:12:01.000Z",
  "title": "Cartan subalgebras in C*-algebras of Hausdorff étale groupoids",
  "authors": [
    "Jonathan H. Brown",
    "Gabriel Nagy",
    "Sarah Reznikoff",
    "Aidan Sims",
    "Dana P. Williams"
  ],
  "comment": "14 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "The reduced C*-algebra of the interior of the isotropy in any Hausdorff \\'etale groupoid G embeds as a C*-subalgebra of the reduced C*-algebra of G. We prove that any representation of the reduced algebra of G that is injective on this subalgebra is faithful. We also show that restriction of functions extends to a faithful conditional expectation of the reduced C*-algebra of G onto the embedded subalgebra, and the set of pure states of the subalgebra with unique extension to the larger C*-algebra is dense. If the interior of the isotropy is abelian, then the embedded subalgebra is a Cartan subalgebra in the sense of Renault.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-11T22:12:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05"
    ],
    "keywords": [
      "cartan subalgebra",
      "hausdorff etale groupoid",
      "embedded subalgebra",
      "faithful conditional expectation",
      "pure states"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150303521B"
    }
  }
}