{
  "id": "physics/9702032",
  "version": "v1",
  "published": "1997-02-24T13:26:17.000Z",
  "updated": "1997-02-24T13:26:17.000Z",
  "title": "Casimir invariants for the complete family of quasi-simple orthogonal algebras",
  "authors": [
    "Francisco J. Herranz",
    "Mariano Santander"
  ],
  "comment": "19 pages, LaTeX",
  "journal": "J.Phys.A30:5411-5426,1997",
  "doi": "10.1088/0305-4470/30/15/026",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "A complete choice of generators of the center of the enveloping algebras of real quasi-simple Lie algebras of orthogonal type, for arbitrary dimension, is obtained in a unified setting. The results simultaneously include the well known polynomial invariants of the pseudo-orthogonal algebras $so(p,q)$, as well as the Casimirs for many non-simple algebras such as the inhomogeneous $iso(p,q)$, the Newton-Hooke and Galilei type, etc., which are obtained by contraction(s) starting from the simple algebras $so(p,q)$. The dimension of the center of the enveloping algebra of a quasi-simple orthogonal algebra turns out to be the same as for the simple $so(p,q)$ algebras from which they come by contraction. The structure of the higher order invariants is given in a convenient \"pyramidal\" manner, in terms of certain sets of \"Pauli-Lubanski\" elements in the enveloping algebras. As an example showing this approach at work, the scheme is applied to recovering the Casimirs for the (3+1) kinematical algebras. Some prospects on the relevance of these results for the study of expansions are also given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1997-02-24T13:26:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "casimir invariants",
      "complete family",
      "enveloping algebra",
      "real quasi-simple lie algebras",
      "quasi-simple orthogonal algebra turns"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 440867
    }
  }
}