{
  "id": "2206.07943",
  "version": "v1",
  "published": "2022-06-16T06:27:17.000Z",
  "updated": "2022-06-16T06:27:17.000Z",
  "title": "Cohomology of $\\frak{sl}(2)$ and its applications in prime characteristic",
  "authors": [
    "Shujuan Wang",
    "Zhaoxin Li"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Over a field of characteristic $p>2,$ the first cohomology of the 3-dimensional simple Lie algebra $\\frak{sl}(2)$ with coefficients in all simple modules is determined, which implies Whitehead's first lemma is not true in prime characteristic. As applications, derivations and 2-local derivations of $\\frak{sl}(2)$ on any simple module are also be characterized.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-16T06:27:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B40",
      "17B50",
      "17B56"
    ],
    "keywords": [
      "prime characteristic",
      "applications",
      "implies whiteheads first lemma",
      "simple module",
      "simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}