{
  "id": "math/0012164",
  "version": "v2",
  "published": "2000-12-18T12:12:01.000Z",
  "updated": "2001-11-07T09:19:06.000Z",
  "title": "Bialgebroids, $\\times_{A}$-bialgebras and duality",
  "authors": [
    "Tomasz Brzezinski",
    "Gigel Militaru"
  ],
  "comment": "16 pages, LaTeX; more concise presentation; Theorem 4.1 improved; final version to appear in J. Algebra",
  "categories": [
    "math.QA",
    "math.RA"
  ],
  "abstract": "An equivalence between Lu's bialgebroids, Xu's bialgebroids with an anchor and Takeuchi's $\\times_{A}$-bialgebras is explicitly proven. A new class of examples of bialgebroids is constructed. A (formal) dual of a bialgebroid, termed bicoalgebroid, is defined. A weak Hopf algebra is shown to be an example of such a bicoalgebroid.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-11-07T09:19:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bialgebras",
      "weak hopf algebra",
      "lus bialgebroids",
      "xus bialgebroids",
      "explicitly proven"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....12164B"
    }
  }
}