{
  "id": "1011.5045",
  "version": "v1",
  "published": "2010-11-23T10:05:56.000Z",
  "updated": "2010-11-23T10:05:56.000Z",
  "title": "The closure of a sheet is not always a union of sheets",
  "authors": [
    "Michael Bulois"
  ],
  "comment": "short note, 3 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note we answer to a frequently asked question. If G is an algebraic group acting on a variety V, a G-sheet of V is an irreducible component of V^(m), the set of elements of V whose G-orbit has dimension m. We focus on the case of the adjoint action of a semisimple group on its Lie algebra. We give two families of examples of sheets whose closure is not a union of sheets in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-11-23T10:05:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B45",
      "20G05"
    ],
    "keywords": [
      "lie algebra",
      "semisimple group",
      "adjoint action",
      "irreducible component",
      "algebraic group acting"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1011.5045B"
    }
  }
}