{
  "id": "math-ph/0008036",
  "version": "v3",
  "published": "2000-08-25T13:45:40.000Z",
  "updated": "2000-11-29T10:26:40.000Z",
  "title": "Functoriality and Morita equivalence of operator algebras and Poisson manifolds associated to groupoids",
  "authors": [
    "N. P. Landsman"
  ],
  "comment": "23 pages, results on measured groupoids and von Neumann algebras added",
  "categories": [
    "math-ph",
    "math.MP",
    "math.OA",
    "math.SG"
  ],
  "abstract": "It is well known that a measured groupoid G defines a von Neumann algebra W*(G), and that a Lie groupoid G canonically defines both a C*-algebra C*(G) and a Poisson manifold A*(G). We show that the maps G -> W*(G), G -> C*(G) and G -> A*(G) are functorial with respect to suitable categories. In these categories Morita equivalence is isomorphism of objects, so that these maps preserve Morita equivalence.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2000-11-29T10:26:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L08",
      "22A22",
      "53D17"
    ],
    "keywords": [
      "poisson manifolds",
      "operator algebras",
      "maps preserve morita equivalence",
      "functoriality",
      "von neumann algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.ph...8036L"
    }
  }
}