{
  "id": "math/9808081",
  "version": "v1",
  "published": "1998-08-17T21:37:54.000Z",
  "updated": "1998-08-17T21:37:54.000Z",
  "title": "Double Lie algebroids and the double of a Lie bialgebroid",
  "authors": [
    "K. C. H. Mackenzie"
  ],
  "comment": "19 pages, LaTeX",
  "categories": [
    "math.DG"
  ],
  "abstract": "We define a general notion of abstract double Lie algebroid. We show (1) that the double Lie algebroid of a double Lie groupoid is a double Lie algebroid in this sense; (2) that the double cotangent constructed from Lie algebroid structures on a vector bundle A and its dual A* is a double Lie algebroid if and only if (A, A*) is a Lie bialgebroid; (3) that a vacant double Lie algebroid structure is equivalent to a matched pair structure on the side Lie algebroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-08-17T21:37:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58H05",
      "17B66",
      "18D05",
      "22A22",
      "58F05"
    ],
    "keywords": [
      "lie bialgebroid",
      "vacant double lie algebroid structure",
      "abstract double lie algebroid",
      "side lie algebroids",
      "double lie groupoid"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......8081M"
    }
  }
}