{
  "id": "math/0010005",
  "version": "v1",
  "published": "2000-10-01T20:06:30.000Z",
  "updated": "2000-10-01T20:06:30.000Z",
  "title": "Presenting Schur algebras as quotients of the universal enveloping algebra of gl(2)",
  "authors": [
    "Stephen Doty",
    "Anthony Giaquinto"
  ],
  "comment": "22 pages; submitted to Algebras and Representation Theory",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We give a presentation of Schur algebras (over the rational number field) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the process we find a new basis for Schur algebras, a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-10-01T20:06:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S30",
      "16P10"
    ],
    "keywords": [
      "universal enveloping algebra",
      "presenting schur algebras",
      "rational number field",
      "integral schur algebra",
      "simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math.....10005D"
    }
  }
}