{
  "id": "1611.05334",
  "version": "v1",
  "published": "2016-11-15T17:34:09.000Z",
  "updated": "2016-11-15T17:34:09.000Z",
  "title": "Reconstruction from Representations: Jacobi via Cohomology",
  "authors": [
    "Boris Kruglikov",
    "Henrik Winther"
  ],
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "A subalgebra of a Lie algebra $\\mathfrak{h}\\subset\\mathfrak{g}$ determines $\\mathfrak{h}$-representation $\\rho$ on $\\mathfrak{m}=\\mathfrak{g}/\\mathfrak{h}$. In this note we discuss how to reconstruct $\\mathfrak{g}$ from $(\\mathfrak{h},\\mathfrak{m},\\rho)$. In other words, we find all the ingredients for building non-reductive Klein geometries. The Lie algebra cohomology plays a decisive role here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-11-15T17:34:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56"
    ],
    "keywords": [
      "representation",
      "reconstruction",
      "lie algebra cohomology plays",
      "building non-reductive klein geometries",
      "ingredients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}