{
  "id": "0712.3764",
  "version": "v4",
  "published": "2007-12-21T18:10:34.000Z",
  "updated": "2009-04-06T19:55:59.000Z",
  "title": "Vanishing of trace forms in low characteristics",
  "authors": [
    "Skip Garibaldi",
    "Alexander Premet"
  ],
  "comment": "Slightly revised since v3. Added short section 8 on Richardson's condition",
  "journal": "Algebra & Number Theory, vol. 3, #5 (2009), 543-566",
  "categories": [
    "math.RT"
  ],
  "abstract": "Every finite-dimensional representation of an algebraic group G gives a trace symmetric bilinear form on the Lie algebra of G. We give criteria in terms of root system data for the existence of a representation such that this form is nonzero or nondegenerate. As a corollary, we show that a Lie algebra of type E8 over a field of characteristic 5 does not have a so-called \"quotient trace form\", answering a question posed in the 1960s.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-04-06T19:55:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "17B50",
      "17B25"
    ],
    "keywords": [
      "low characteristics",
      "lie algebra",
      "trace symmetric bilinear form",
      "root system data",
      "quotient trace form"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3764G"
    }
  }
}