{
  "id": "2007.14692",
  "version": "v1",
  "published": "2020-07-29T09:19:50.000Z",
  "updated": "2020-07-29T09:19:50.000Z",
  "title": "Lie algebra of homogeneous operators of a vector bundle",
  "authors": [
    "P. B. A. Lecomte",
    "Elie Zihindula Mushengezi"
  ],
  "comment": "13 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We prove that for a vector bundle E, the Lie algebra De(E) generated by all differential operators on E which are eigenvectors of the Lie derivative in the direction of the Euler vector field of E and the Lie algebra Dg(E) obtained by Grothendieck construction over the R-algebra A(E):= Pol(E), coincide. This allows us to compute all the derivations of A(E) and to obtain a Lie algebraic charaterization of the vector bundle E with the Lie algebra of zero-weight derivations of the R-algebra A(E).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-29T09:19:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "vector bundle",
      "homogeneous operators",
      "lie algebraic charaterization",
      "euler vector field",
      "lie algebra dg"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}