{
  "id": "1104.1378",
  "version": "v1",
  "published": "2011-04-07T16:57:19.000Z",
  "updated": "2011-04-07T16:57:19.000Z",
  "title": "Dirac pairs",
  "authors": [
    "Yvette Kosmann-Schwarzbach"
  ],
  "comment": "dedicated to Tudor Ratiu, 23 pages",
  "journal": "J. Geom. Mechanics, 4(2) (2012), 165-180",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We extend the definition of the Nijenhuis torsion of an endomorphism of a Lie algebroid to that of a relation, and we prove that the torsion of the relation defined by a bi-Hamiltonian structure vanishes. Following Gelfand and Dorfman, we then define Dirac pairs, and we analyze the relationship of this general notion with the various kinds of compatible structures on manifolds, more generally on Lie algebroids.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-07T16:57:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D17",
      "53D18",
      "37K10",
      "17B63"
    ],
    "keywords": [
      "lie algebroid",
      "define dirac pairs",
      "bi-hamiltonian structure vanishes",
      "nijenhuis torsion",
      "general notion"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.1378K"
    }
  }
}