{
  "id": "math/0309274",
  "version": "v1",
  "published": "2003-09-17T12:26:31.000Z",
  "updated": "2003-09-17T12:26:31.000Z",
  "title": "Towards a classification of Lorentzian holonomy groups. Part II: Semisimple, non-simple weak-Berger algebras",
  "authors": [
    "Thomas Leistner"
  ],
  "comment": "13 pages",
  "journal": "J. Differential Geom. 76 (2007), no. 3, 423-484",
  "categories": [
    "math.DG"
  ],
  "abstract": "The holonomy group of an (n+2)-dimensional simply-connected, indecomposable but non-irreducible Lorentzian manifold (M,h) is contained in the parabolic group $(\\mathbb{R} \\times SO(n))\\ltimes \\mathbb{R}^n$. The main ingredient of such a holonomy group is the SO(n)--projection $G:=pr_{SO(n)}(Hol_p(M,h))$ and one may ask whether it has to be a Riemannian holonomy group. In this paper we show that this is always the case, completing our results of the first part math.DG/0305139. We draw consequences for the existence of parallel spinors on Lorentzian manifolds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-09-17T12:26:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53B30",
      "53C50",
      "53C27",
      "53C29"
    ],
    "keywords": [
      "non-simple weak-berger algebras",
      "lorentzian holonomy groups",
      "classification",
      "semisimple",
      "riemannian holonomy group"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......9274L"
    }
  }
}