{
  "id": "math/0209275",
  "version": "v1",
  "published": "2002-09-20T18:14:14.000Z",
  "updated": "2002-09-20T18:14:14.000Z",
  "title": "Simplicity of Rings of Differential Operators in Prime Characteristic",
  "authors": [
    "Karen E. Smith",
    "Michel Van den Bergh"
  ],
  "comment": "30 pages; Latex file; One minor difference between this version and published version: Incorrect justification for one easy statement in proof of Proposition 3.1.6 corrected",
  "journal": "Proc. London Math. Soc. (3) 75 (1997), no. 1, 32--62",
  "categories": [
    "math.RT",
    "math.AC",
    "math.RA"
  ],
  "abstract": "Let W be a finite dimensional representation of a linearly reductive group G over a field k. Motivated by their work on classical rings of invariants, Levasseur and Stafford asked whether the ring of invariants under G of the symmetric algebra of W has a simple ring of differential operators. In this paper, we show that this is true in prime characteristic. Indeed, if R is a graded subring of a polynomial ring over a perfect field of characteristic p>0 and if the inclusionof R into S splits, then D_k(R) is a simple ring. In the last section of the paper, we discuss how one might try to deduce the characteristic zero case from this result. As yet, however, this is a subtle problem and the answer to the question of Levasseur and Stafford remains open in characteristic zero.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-09-20T18:14:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S32",
      "16G60",
      "13A35"
    ],
    "keywords": [
      "prime characteristic",
      "differential operators",
      "simplicity",
      "characteristic zero case",
      "stafford remains open"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9275S"
    }
  }
}