{
  "id": "1812.09539",
  "version": "v1",
  "published": "2018-12-22T14:57:42.000Z",
  "updated": "2018-12-22T14:57:42.000Z",
  "title": "Quantized $SL(2)$ representations of knot groups",
  "authors": [
    "Jun Murakami",
    "Roland van der Veen"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "A quantum deformation of the space of $SL(2)$ representations of knot groups is constructed using the braided quantum group $BSL(2)$ introduced by S. Majid, which is a quantum analogue of the group $SL(2)$ obtained by quantizing the coordinate ring of $SL(2)$ and also quantizing the flip of the tensor product by changing it to a braiding. This construction works for any braided Hopf algebra satisfying braided commutativity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-22T14:57:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "57M05",
      "16T05"
    ],
    "keywords": [
      "knot groups",
      "representations",
      "hopf algebra satisfying braided commutativity",
      "braided quantum group",
      "quantum deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}