{
  "id": "1912.03686",
  "version": "v1",
  "published": "2019-12-08T14:32:07.000Z",
  "updated": "2019-12-08T14:32:07.000Z",
  "title": "Intermediate C*-algebras of Cartan Embeddings",
  "authors": [
    "Jonathan H. Brown",
    "Ruy Exel",
    "Adam H. Fuller",
    "David R. Pitts",
    "Sarah A. Reznikodff"
  ],
  "comment": "14 pages",
  "categories": [
    "math.OA"
  ],
  "abstract": "Let $A$ be a C$^*$-algebra and let $D$ be a Cartan subalgebra of $A$. We study the following question: if $B$ is a C$^*$-algebra such that $D \\subseteq B \\subseteq A$, is $D$ a Cartan subalgebra of $B$? We give a positive answer in two cases: the case when there is a faithful conditional expectation from $A$ onto $B$, and the case when $A$ is nuclear and $D$ is a C$^*$-diagonal of $A$. In both cases there is a one-to-one correspondence between the intermediate C$^*$-algebras $B$, and a class of open subgroupoids of the groupoid $G$, where $\\Sigma \\rightarrow G$ is the twist associated with the embedding $D \\subseteq A$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-08T14:32:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "22A22",
      "46L55"
    ],
    "keywords": [
      "cartan embeddings",
      "intermediate",
      "cartan subalgebra",
      "one-to-one correspondence",
      "open subgroupoids"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}