{
  "id": "1711.05931",
  "version": "v1",
  "published": "2017-11-16T05:25:03.000Z",
  "updated": "2017-11-16T05:25:03.000Z",
  "title": "$A_2$ Skein Representations of Pure Braid Groups",
  "authors": [
    "Wataru Yuasa"
  ],
  "comment": "13 pages, many TikZ pictures",
  "categories": [
    "math.GT",
    "math.GR",
    "math.QA"
  ],
  "abstract": "We define a family of representations $\\{\\rho_n\\}_{n\\geq 0}$ of a pure braid group $P_{2k}$. These representations are obtained from an action of $P_{2k}$ on a certain type of $A_2$ web space with color $n$. The $A_2$ web space is a generalization of the Kauffman bracket skein module of a disk with marked points on its boundary. We also introduce a triangle-free basis of such an $A_2$ web space and calculate matrix representations of $\\rho_n$ about the standard generators of $P_{2k}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-16T05:25:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "57M99"
    ],
    "keywords": [
      "pure braid group",
      "skein representations",
      "web space",
      "kauffman bracket skein module",
      "triangle-free basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}