{
  "id": "math/0310020",
  "version": "v1",
  "published": "2003-10-02T11:37:41.000Z",
  "updated": "2003-10-02T11:37:41.000Z",
  "title": "Generators of algebraic covariant derivative curvature tensors and Young symmetrizers",
  "authors": [
    "B. Fiedler"
  ],
  "comment": "18 pages. Chapter for a book \"Progress in Computer Science Research\", in preparation by Nova Science Publishers, Inc.: http://www.novapublishers.com/",
  "journal": "In: Leading-Edge Computer Science, S. Shannon (ed.), Nova Science Publishers, Inc. New York, 2006. pp. 219-239. ISBN: 1-59454-526-X",
  "categories": [
    "math.CO",
    "cs.SC",
    "math.DG"
  ],
  "abstract": "We show that the space of algebraic covariant derivative curvature tensors R' is generated by Young symmetrized tensor products W*U or U*W, where W and U are covariant tensors of order 2 and 3 whose symmetry classes are irreducible and characterized by the following pairs of partitions: {(2),(3)}, {(2),(2 1)} or {(1 1),(2 1)}. Each of the partitions (2), (3) and (1 1) describes exactly one symmetry class, whereas the partition (2 1) characterizes an infinite set S of irreducible symmetry classes. This set S contains exactly one symmetry class S_0 whose elements U can not play the role of generators of tensors R'. The tensors U of all other symmetry classes from S\\{S_0} can be used as generators for tensors R'. Foundation of our investigations is a theorem of S. A. Fulling, R. C. King, B. G. Wybourne and C. J. Cummins about a Young symmetrizer that generates the symmetry class of algebraic covariant derivative curvature tensors. Furthermore we apply ideals and idempotents in group rings C[Sr], the Littlewood-Richardson rule and discrete Fourier transforms for symmetric groups Sr. For certain symbolic calculations we used the Mathematica packages Ricci and PERMS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-02T11:37:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B20",
      "15A72",
      "05E10",
      "16D60",
      "05-04"
    ],
    "keywords": [
      "algebraic covariant derivative curvature tensors",
      "young symmetrizer",
      "symmetry classes",
      "generators",
      "symmetric groups sr"
    ],
    "tags": [
      "book chapter",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10020F"
    }
  }
}