{
  "id": "2211.14756",
  "version": "v1",
  "published": "2022-11-27T08:03:54.000Z",
  "updated": "2022-11-27T08:03:54.000Z",
  "title": "The Jucys-Murphy basis and semisimplicty criteria for the $q$-Brauer algebra",
  "authors": [
    "Hebing Rui",
    "Mei Si",
    "Linliang Song"
  ],
  "comment": "21 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We construct the Jucys-Murphy elements and the Jucys-Murphy basis for the $q$-Brauer algebra in the sense of Mathas[11]. We also give a necessary and sufficient condition for the $q$-Brauer algebra being (split) semisimple over an arbitrary field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-27T08:03:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "brauer algebra",
      "jucys-murphy basis",
      "semisimplicty criteria",
      "jucys-murphy elements",
      "sufficient condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}