{
  "id": "1812.01587",
  "version": "v1",
  "published": "2018-12-04T18:42:50.000Z",
  "updated": "2018-12-04T18:42:50.000Z",
  "title": "A Projective Representations of the Thompson Group F and Its Lifting Problem",
  "authors": [
    "Jun Yang"
  ],
  "comment": "18 pages, 3 figures",
  "categories": [
    "math.RT",
    "math.GR"
  ],
  "abstract": "The Thompson group $F$ has a canonical unitary representation on $H=L^2[0,1]$. With a special projection, we construct a projective unitary representation on a Fermionic Fock space associated with $H$. This comes from the representation of the CAR algebra of $H$. Then, by computing the 2nd cohomology group, we know this projective unitary representation may cannot be lifted to a unitary one. We will mainly discuss the lifting problem of this projective representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-04T18:42:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "thompson group",
      "projective representation",
      "lifting problem",
      "projective unitary representation",
      "fermionic fock space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}