{
  "id": "1705.06685",
  "version": "v1",
  "published": "2017-05-18T16:41:42.000Z",
  "updated": "2017-05-18T16:41:42.000Z",
  "title": "Representations of the Lie algebra of vector fields on a sphere",
  "authors": [
    "Yuly Billig",
    "Jonathan Nilsson"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "For an affine algebraic variety $X$ we study a category of modules that admit compatible actions of both the algebra of functions on $X$ and the Lie algebra of vector fields on $X$. In particular, for the case when $X$ is the sphere $\\mathbb{S}^2$, we construct a set of simple modules that are finitely generated over $A$. In addition, we prove that the monoidal category that these modules generate is equivalent to the category of finite-dimensional rational $\\mathrm{GL}_2$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-18T16:41:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B66"
    ],
    "keywords": [
      "vector fields",
      "lie algebra",
      "representations",
      "affine algebraic variety",
      "modules generate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}