{
  "id": "1902.02002",
  "version": "v1",
  "published": "2019-02-06T02:13:37.000Z",
  "updated": "2019-02-06T02:13:37.000Z",
  "title": "Dimension and Trace of the Kauffman Bracket Skein Algebra",
  "authors": [
    "Charles Frohman",
    "Joanna Kania-Bartosynska",
    "Thang Le"
  ],
  "comment": "42 pages, 5 figures",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "Let $F$ be a finite type surface and $\\zeta$ a complex root of unity. The Kauffman bracket skein algebra $K_{\\zeta}(F)$ is an important object in both classical and quantum topology as it has relations to the character variety, the Teichm\\\"uller space, the Jones polynomial, and the Witten-Reshetikhin-Turaev Topological Quantum Field Theories. We compute the rank and trace of $K_{\\zeta}(F)$ over its center, and we extend a theorem of Frohman and Kania-Bartoszynska which says the skein algebra has a splitting coming from two pants decompositions of $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T02:13:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27"
    ],
    "keywords": [
      "kauffman bracket skein algebra",
      "witten-reshetikhin-turaev topological quantum field theories",
      "finite type surface",
      "complex root",
      "character variety"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}