{
  "id": "math/0210384",
  "version": "v1",
  "published": "2002-10-24T14:56:18.000Z",
  "updated": "2002-10-24T14:56:18.000Z",
  "title": "On certain canonical diffeomorphisms in symplectic and Poisson geometry",
  "authors": [
    "K. C. H. Mackenzie"
  ],
  "comment": "12 pages. To appear in `Quantization, Poisson brackets and beyond', proceedings of a conference at UMIST (UK) in July 2001, edited by Ted Voronov, Contemporary Mathematics",
  "categories": [
    "math.DG",
    "math.SG"
  ],
  "abstract": "The canonical involution of a double (=iterated) tangent bundle may be dualized in different ways to yield relations between the Tulczyjew diffeomorphism, the Poisson anchor associated with the standard symplectic structure on the cotangent space,and the reversal diffeomorphism. We show that the constructions which yield these maps extend very generally to the double Lie algebroids of double Lie groupoids, where they play a crucial role in the relations between double Lie algebroids and Lie bialgebroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-24T14:56:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "58H01",
      "17B66",
      "18D05",
      "22A22",
      "58F05"
    ],
    "keywords": [
      "poisson geometry",
      "canonical diffeomorphisms",
      "double lie algebroids",
      "standard symplectic structure",
      "yield relations"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10384M"
    }
  }
}