{
  "id": "math/0201243",
  "version": "v2",
  "published": "2002-01-25T11:26:56.000Z",
  "updated": "2002-12-10T19:02:33.000Z",
  "title": "Computation of Centralizers in Braid groups and Garside Groups",
  "authors": [
    "Nuno Franco",
    "Juan Gonzalez-Meneses"
  ],
  "comment": "The algorithm has been improved by using the Summit Class, instead of the conjugacy class of the element under study. The word \"normalizer\" has been replaced by \"centralizer\". 14 pages, 4 figures",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "We give a new method to compute the centralizer of an element in Artin braid groups and, more generally, in Garside groups. This method, together with the solution of the conugacy problem given by the authors in a previous paper, are two main steps for solving conjugacy systems, thus breaking recently discovered cryptosystems based in braid groups. We also present the result of our computations, where we notice that our algorithm yields surprisingly small generating sets for the centralizers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-10T19:02:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "garside groups",
      "centralizer",
      "computation",
      "yields surprisingly small generating sets",
      "artin braid groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......1243F"
    }
  }
}