{
  "id": "1509.06280",
  "version": "v1",
  "published": "2015-09-21T15:44:56.000Z",
  "updated": "2015-09-21T15:44:56.000Z",
  "title": "On Gelfand-Kirillov conjecture for some W-algebras",
  "authors": [
    "Alexey Petukhov"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Consider the W-algebra $W$ attached to the smallest nilpotent orbit in a simple Lie algebra $\\frak g$ over an algebraically closed field of characteristic 0. We show that if an analogue of the Gelfand-Kirillov conjecture holds for such a W-algebra then it holds for the universal enveloping algebra $\\mathrm U(\\frak g)$. This together with a result of A. Premet implies that the analogue of the Gelfand-Kirillov conjecture fails for some $W$-algebras attached to some nilpotent orbits in Lie algebras of types $B_n~(n\\ge 3)$, $D_n~(n\\ge 4)$, $E_6, E_7, E_8$, $F_4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-21T15:44:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simple lie algebra",
      "smallest nilpotent orbit",
      "gelfand-kirillov conjecture holds",
      "gelfand-kirillov conjecture fails",
      "universal enveloping algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150906280P"
    }
  }
}