{
  "id": "0811.2951",
  "version": "v2",
  "published": "2008-11-18T16:39:04.000Z",
  "updated": "2015-04-28T16:28:55.000Z",
  "title": "Automorphisms of cotangent bundles of Lie groups",
  "authors": [
    "Andre Diatta",
    "Bakary Manga"
  ],
  "comment": "V2: 27 pages, Latex, a few minor results added and the paper layout reorganised. The last version appeared at Afr. Diaspora J. Math",
  "journal": "Afr. Diaspora J. Math. 17, no 2 (2014), 20-46",
  "categories": [
    "math.DG",
    "math.GR"
  ],
  "abstract": "Let G be a Lie group, $T^*G$ its cotangent bundle with its natural Lie group structure obtained by performing a left trivialization of T^*G and endowing the resulting trivial bundle with the semi-direct product, using the coadjoint action of G on the dual space of its Lie algebra. We investigate the group of automorphisms of the Lie algebra of $T^*G$. More precisely, amongst other results, we fully characterize the space of all derivations of the Lie algebra of $T^*G$. As a byproduct, we also characterize some spaces of operators on G amongst which, the space J of bi-invariant tensors on G and prove that if G has a bi-invariant Riemannian or pseudo-Riemannian metric, then J is isomorphic to the space of linear maps from the Lie algebra of G to its dual space which are equivariant with respect to the adjoint and coadjoint actions, as well as that of bi-invariant bilinear forms on G. We discuss some open problems and possible applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-11-18T16:39:04.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-04-28T16:28:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22C05",
      "22E60",
      "22E15",
      "22E10"
    ],
    "keywords": [
      "cotangent bundle",
      "lie algebra",
      "automorphisms",
      "coadjoint action",
      "dual space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.2951D"
    }
  }
}