{
  "id": "math-ph/0211008",
  "version": "v2",
  "published": "2002-11-05T20:00:08.000Z",
  "updated": "2002-11-17T23:48:58.000Z",
  "title": "Noncommutative de Rham cohomology of finite groups",
  "authors": [
    "L. Castellani",
    "R. Catenacci",
    "M. Debernardi",
    "C. Pagani"
  ],
  "comment": "LaTeX, 25 pages, 4 figures. Added higher order exterior basis and volume forms of quaternion and dihedral groups, corrected sign in eq. (2.37) and (2.40), corrected misprints",
  "journal": "Int.J.Mod.Phys. A19 (2004) 1961-1986",
  "doi": "10.1142/S0217751X04018403",
  "categories": [
    "math-ph",
    "hep-th",
    "math.DG",
    "math.MP",
    "math.QA"
  ],
  "abstract": "We study de Rham cohomology for various differential calculi on finite groups G up to order 8. These include the permutation group S_3, the dihedral group D_4 and the quaternion group Q. Poincare' duality holds in every case, and under some assumptions (essentially the existence of a top form) we find that it must hold in general. A short review of the bicovariant (noncommutative) differential calculus on finite G is given for selfconsistency. Exterior derivative, exterior product, metric, Hodge dual, connections, torsion, curvature, and biinvariant integration can be defined algebraically. A projector decomposition of the braiding operator is found, and used in constructing the projector on the space of 2-forms. By means of the braiding operator and the metric a knot invariant is defined for any finite group.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-11-17T23:48:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite group",
      "rham cohomology",
      "differential calculus",
      "braiding operator",
      "noncommutative"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "International Journal of Modern Physics A",
      "year": 2004,
      "volume": 19,
      "number": 12,
      "pages": 1961
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 602405,
      "adsabs": "2004IJMPA..19.1961C"
    }
  }
}