{
  "id": "math/0212278",
  "version": "v2",
  "published": "2002-12-19T20:26:42.000Z",
  "updated": "2002-12-23T18:25:04.000Z",
  "title": "Determination of the structure of algebraic curvature tensors by means of Young symmetrizers",
  "authors": [
    "B. Fiedler"
  ],
  "comment": "19 pages. To appear Seminaire Lotharingien de Combinatoire: http://www.mat.univie.ac.at/~slc/",
  "journal": "Seminaire Lotharingien de Combinatoire, 48 (2003) Article B48d",
  "categories": [
    "math.CO",
    "cs.SC",
    "math.DG"
  ],
  "abstract": "For a positive definite fundamental tensor all known examples of Osserman algebraic curvature tensors have a typical structure. They can be produced from a metric tensor and a finite set of skew-symmetric matrices which fulfil Clifford commutation relations. We show by means of Young symmetrizers and a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins that every algebraic curvature tensor has a structure which is very similar to that of the above Osserman curvature tensors. We verify our results by means of the Littlewood-Richardson rule and plethysms. For certain symbolic calculations we used the Mathematica packages MathTensor, Ricci and PERMS.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-12-23T18:25:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B20",
      "15A72",
      "05E10",
      "16D60",
      "05-04"
    ],
    "keywords": [
      "young symmetrizers",
      "determination",
      "fulfil clifford commutation relations",
      "osserman algebraic curvature tensors",
      "osserman curvature tensors"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....12278F"
    }
  }
}