{
  "id": "1907.05670",
  "version": "v1",
  "published": "2019-07-12T10:47:46.000Z",
  "updated": "2019-07-12T10:47:46.000Z",
  "title": "Deformations of Vector Bundles over Lie Groupoids",
  "authors": [
    "Pier Paolo La Pastina",
    "Luca Vitagliano"
  ],
  "comment": "39 pages. Comments welcome!!",
  "categories": [
    "math.DG",
    "math.RT",
    "math.SG"
  ],
  "abstract": "VB-groupoids are vector bundles in the category of Lie groupoids. They encompass several classical objects, including Lie group representations and 2-vector spaces. Moreover, they provide geometric pictures for 2-term representations up to homotopy of Lie groupoids. We attach to every VB-groupoid a cochain complex controlling its deformations and discuss its fundamental features, such as Morita invariance and a van Est theorem. Several examples and applications are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-12T10:47:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A22",
      "58H05",
      "58H15"
    ],
    "keywords": [
      "lie groupoids",
      "vector bundles",
      "deformations",
      "lie group representations",
      "fundamental features"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}