{
  "id": "1904.04915",
  "version": "v1",
  "published": "2019-04-09T21:16:30.000Z",
  "updated": "2019-04-09T21:16:30.000Z",
  "title": "Cartan Connections and Atiyah Lie Algebroids",
  "authors": [
    "Jeremy Attard",
    "Jordan François",
    "Serge Lazzarini",
    "Thierry Masson"
  ],
  "comment": "27 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "This work extends previous developments carried out by some of the authors on Ehresmann connections on Atiyah Lie algebroids. In this paper, we study Cartan connections in a framework relying on two Atiyah Lie algebroids based on a $H$-principal fiber bundle $\\mathcal{P}$ and its associated $G$-principal fiber bundle $\\mathcal{Q} := \\mathcal{P} \\times_H G$, where $H \\subset G$ defines the model for a Cartan geometry. The first main result of this study is a commutative and exact diagram relating these two Atiyah Lie algebroids, which allows to completely characterize Cartan connections on $\\mathcal{P}$. Furthermore, in the context of gravity and mixed anomalies, our construction answers a long standing mathematical question about the correct geometrico-algebraic setting in which to combine inner gauge transformations and infinitesimal diffeomorphisms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-09T21:16:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51P05",
      "70S15",
      "70S20",
      "83C99"
    ],
    "keywords": [
      "atiyah lie algebroids",
      "principal fiber bundle",
      "first main result",
      "inner gauge transformations",
      "study cartan connections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}