{
  "id": "0803.2284",
  "version": "v1",
  "published": "2008-03-15T11:14:15.000Z",
  "updated": "2008-03-15T11:14:15.000Z",
  "title": "Cartan subalgebras in C*-algebras",
  "authors": [
    "Jean Renault"
  ],
  "comment": "21 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "According to J. Feldman and C. Moore's well-known theorem on Cartan subalgebras, a variant of the group measure space construction gives an equivalence of categories between twisted countable standard measured equivalence relations and Cartan pairs, i.e. a von Neumann algebra (on a separable Hilbert space) together with a Cartan subalgebra. A. Kumjian gave a C*-algebraic analogue of this theorem in the early eighties. After a short survey of maximal abelian self-adjoint subalgebras in operator algebras, I present a natural definition of a Cartan subalgebra in a C*-algebra and an extension of Kumjian's theorem which covers graph algebras and some foliation algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-15T11:14:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37D35",
      "46L85"
    ],
    "keywords": [
      "cartan subalgebra",
      "maximal abelian self-adjoint subalgebras",
      "group measure space construction",
      "von neumann algebra",
      "moores well-known theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.2284R"
    }
  }
}