{
  "id": "0802.2314",
  "version": "v2",
  "published": "2008-02-16T05:28:14.000Z",
  "updated": "2009-02-12T10:59:31.000Z",
  "title": "Injectivity on the set of conjugacy classes of some monomorphisms between Artin groups",
  "authors": [
    "Eon-Kyung Lee",
    "Sang-Jin Lee"
  ],
  "comment": "27 pages, 16 figures, published version",
  "journal": "Journal of Algebra, vol. 323, no. 7, pp. 1879-1907, 2010",
  "doi": "10.1016/j.jalgebra.2008.12.013",
  "categories": [
    "math.GT",
    "math.GR"
  ],
  "abstract": "There are well-known monomorphisms between the Artin groups of finite type $\\arA_n$, $\\arB_n=\\arC_n$ and affine type $\\tilde \\arA_{n-1}$, $\\tilde\\arC_{n-1}$. The Artin group $A(\\arA_n)$ is isomorphic to the $(n+1)$-strand braid group $B_{n+1}$, and the other three Artin groups are isomorphic to some subgroups of $B_{n+1}$. The inclusions between these subgroups yield monomorphisms $A(\\arB_n)\\to A(\\arA_n)$, $A(\\tilde \\arA_{n-1})\\to A(\\arB_n)$ and $A(\\tilde \\arC_{n-1})\\to A(\\arB_n)$. There are another type of monomorphisms $A(\\arB_d)\\to A(\\arA_{md-1})$, $A(\\arB_d)\\to A(\\arB_{md})$ and $A(\\arB_d)\\to A(\\arA_{md})$ which are induced by isomorphisms between Artin groups of type $\\arB$ and centralizers of periodic braids. In this paper, we show that the monomorphisms $A(\\arB_d)\\to A(\\arA_{md-1})$, $A(\\arB_d)\\to A(\\arB_{md})$ and $A(\\arB_d)\\to A(\\arA_{md})$ induce injective functions on the set of conjugacy classes, and that none of the monomorphisms $A(\\arB_n)\\to A(\\arA_n)$, $A(\\tilde \\arA_{n-1})\\to A(\\arB_n)$ and $A(\\tilde \\arC_{n-1})\\to A(\\arB_n)$ does so.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-12T10:59:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F36",
      "20F10"
    ],
    "keywords": [
      "artin group",
      "conjugacy classes",
      "injectivity",
      "strand braid group",
      "subgroups yield monomorphisms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0802.2314L"
    }
  }
}