{
  "id": "1108.2366",
  "version": "v1",
  "published": "2011-08-11T10:26:19.000Z",
  "updated": "2011-08-11T10:26:19.000Z",
  "title": "Modular classes of skew algebroid relations",
  "authors": [
    "Janusz Grabowski"
  ],
  "comment": "20 pages",
  "journal": "Transform. Groups 17 (2012), 989-1010",
  "doi": "10.1007/S00031-012-9197-2",
  "categories": [
    "math.DG",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Skew algebroid is a natural generalization of the concept of Lie algebroid. In this paper, for a skew algebroid E, its modular class mod(E) is defined in the classical as well as in the supergeometric formulation. It is proved that there is a homogeneous nowhere-vanishing 1-density on E* which is invariant with respect to all Hamiltonian vector fields if and only if E is modular, i.e. mod(E)=0. Further, relative modular class of a subalgebroid is introduced and studied together with its application to holonomy, as well as modular class of a skew algebroid relation. These notions provide, in particular, a unified approach to the concepts of a modular class of a Lie algebroid morphism and that of a Poisson map.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-08-11T10:26:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D17",
      "17B56",
      "17B63",
      "17B66",
      "17B70",
      "58A32"
    ],
    "keywords": [
      "skew algebroid relation",
      "modular classes",
      "hamiltonian vector fields",
      "modular class mod",
      "lie algebroid morphism"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1108.2366G"
    }
  }
}