{
  "id": "1709.08863",
  "version": "v1",
  "published": "2017-09-26T07:02:33.000Z",
  "updated": "2017-09-26T07:02:33.000Z",
  "title": "Representations of Lie algebras of vector fields on affine varieties",
  "authors": [
    "Yuly Billig",
    "Vyacheslav Futorny",
    "Jonathan Nilsson"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "For an irreducible affine variety $X$ over an algebraically closed field of characteristic zero we define two new classes of modules over the Lie algebra of vector fields on $X$ - gauge modules and Rudakov modules, which admit a compatible action of the algebra of functions. Gauge modules are generalizations of modules of tensor densities whose construction was inspired by non-abelian gauge theory. Rudakov modules are generalizations of a family of induced modules over the Lie algebra of derivations of a polynomial ring studied by Rudakov. We prove general simplicity theorems for these two types of modules and establish a pairing between them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-26T07:02:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20",
      "17B66",
      "13N15"
    ],
    "keywords": [
      "lie algebra",
      "vector fields",
      "gauge modules",
      "rudakov modules",
      "representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}