{
  "id": "2405.17617",
  "version": "v1",
  "published": "2024-05-27T19:27:56.000Z",
  "updated": "2024-05-27T19:27:56.000Z",
  "title": "Abelianization of Lie algebroids and Lie groupoids",
  "authors": [
    "Shuyu Xiao"
  ],
  "comment": "22 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "We investigate the abelianization of a Lie algebroid and provide a necessary and sufficient condition for its existence. We also study the abelianization of groupoids and provide sufficient conditions for its existence in the smooth category and a necessary and sufficient condition for its existence in the diffeological category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-27T19:27:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22A22",
      "53D17"
    ],
    "keywords": [
      "lie algebroid",
      "lie groupoids",
      "sufficient condition",
      "abelianization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}