{
  "id": "1808.06395",
  "version": "v1",
  "published": "2018-08-20T11:39:07.000Z",
  "updated": "2018-08-20T11:39:07.000Z",
  "title": "Representations of finite-dimensional quotient algebras of the 3-string braid group",
  "authors": [
    "Pavel Pyatov",
    "Anastasia Trofimova"
  ],
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give semisimplicity criteria for these algebras and present explicit formulas for all their irreducible representations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-20T11:39:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite-dimensional quotient algebras",
      "representations",
      "th order generic polynomial relations",
      "string braid group",
      "group algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}