{
  "id": "1702.02435",
  "version": "v1",
  "published": "2017-02-08T14:16:03.000Z",
  "updated": "2017-02-08T14:16:03.000Z",
  "title": "Dirac operator and its cohomology for the quantum group $U_q(\\mathfrak{sl}_2)$",
  "authors": [
    "Pavle Pandžić",
    "Petr Somberg"
  ],
  "categories": [
    "math.RT",
    "math-ph",
    "math.FA",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We introduce a Dirac operator $D$ for the quantum group $U_q(\\mathfrak{sl}_2)$, as an element of the tensor product of $U_q(\\mathfrak{sl}_2)$ with the Clifford algebra on two generators. We study the properties of $D$, including an analogue of Vogan's conjecture. We compute the cohomology of $D$ acting on various $U_q(\\mathfrak{sl}_2)$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-08T14:16:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T20",
      "20G42"
    ],
    "keywords": [
      "quantum group",
      "dirac operator",
      "cohomology",
      "tensor product",
      "clifford algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}