{
  "id": "math-ph/0212047",
  "version": "v1",
  "published": "2002-12-16T15:51:07.000Z",
  "updated": "2002-12-16T15:51:07.000Z",
  "title": "Development of a unified tensor calculus for the exceptional Lie algebras",
  "authors": [
    "A. J. Macfarlane",
    "Hendryk Pfeiffer"
  ],
  "comment": "27 pages, LaTeX 2e",
  "journal": "Int. J. Mod. Phys. A19:287-316, 2004",
  "doi": "10.1142/S0217751X04017562",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "The uniformity of the decomposition law, for a family F of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^n of their adjoint representations ad is now well-known. This paper uses it to embark on the development of a unified tensor calculus for the exceptional Lie algebras. It deals explicitly with all the tensors that arise at the n=2 stage, obtaining a large body of systematic information about their properties and identities satisfied by them. Some results at the n=3 level are obtained, including a simple derivation of the the dimension and Casimir eigenvalue data for all the constituents of ad^3. This is vital input data for treating the set of all tensors that enter the picture at the n=3 level, following a path already known to be viable for a_1. The special way in which the Lie algebra d_4 conforms to its place in the family F alongside the exceptional Lie algebras is described.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-12-16T15:51:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional lie algebras",
      "unified tensor calculus",
      "development",
      "vital input data",
      "adjoint representations ad"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 924509
    }
  }
}