{
  "id": "math/0410017",
  "version": "v1",
  "published": "2004-10-01T14:10:25.000Z",
  "updated": "2004-10-01T14:10:25.000Z",
  "title": "Representation theory of the Drinfel'd doubles of a family of Hopf algebras",
  "authors": [
    "K. Erdmann",
    "E. L. Green",
    "N. Snashall",
    "R. Taillefer"
  ],
  "comment": "32 pages, uses xy diagrams, submitted",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We investigate the Drinfel'd doubles $D(\\Lambda_{n,d})$ of a certain family of Hopf algebras. We determine their simple modules and their indecomposable projective modules, and we obtain a presentation by quiver and relations of these Drinfel'd doubles, from which we deduce properties of their representations, including the Auslander-Reiten quivers of the $D(\\Lambda_{n,d})$. We then determine decompositions of the tensor products of most of the representations described, and in particular give a complete description of the tensor product of two simple modules. This study also leads to explicit examples of Hopf bimodules over the original Hopf algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-01T14:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "06B15",
      "81R50",
      "16W30",
      "16W35",
      "16G20",
      "16G70",
      "18D10"
    ],
    "keywords": [
      "drinfeld doubles",
      "representation theory",
      "tensor product",
      "simple modules",
      "original hopf algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10017E"
    }
  }
}