{
  "id": "math/0510551",
  "version": "v1",
  "published": "2005-10-26T09:45:05.000Z",
  "updated": "2005-10-26T09:45:05.000Z",
  "title": "$AF$ Embedding of Crossed Products of Certain Graph $C^*$-Algebras by Quasi-free Actions",
  "authors": [
    "Xiaochun Fang"
  ],
  "categories": [
    "math.OA"
  ],
  "abstract": "We introduce the labelling map and the quasi-free action of a locally compact abelian group on a graph $C^*$-algebra of a row-finite directed graph. Some necessary conditions for embedding the crossed product to an $AF$ algebra are discussed, and one sufficient condition is proved that if the row-finite directed graph is constructed by possibly attaching some 1-loops to a row-finite directed graph whose each weak connected component is a rooted (possibly infinite) directed tree, and the labelling map is almost proper, which is proved to be a reasonable generalization of the earlier case, then the crossed product can be embedded to an $AF$ algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-10-26T09:45:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L05",
      "19K33"
    ],
    "keywords": [
      "crossed product",
      "quasi-free action",
      "row-finite directed graph",
      "labelling map",
      "locally compact abelian group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....10551F"
    }
  }
}