{
  "id": "math/0612098",
  "version": "v2",
  "published": "2006-12-04T16:46:22.000Z",
  "updated": "2008-02-09T09:20:14.000Z",
  "title": "(Z/2Z x Z/2Z)-symmetric spaces",
  "authors": [
    "Yuri Bahturin",
    "Michel Goze"
  ],
  "comment": "31 pages",
  "categories": [
    "math.DG",
    "math.RA"
  ],
  "abstract": "The notion of a $\\Gamma $-symmetric space is a generalization of the classical notion of a symmetric space, where a general finite abelian group $\\Gamma $ replaces the group $Z_2$. The case $\\Gamma =\\Z_k$ has also been studied, from the algebraic point of view by V.Kac \\cite{VK} and from the point of view of the differential geometry by Ledger, Obata, Kowalski or Wolf - Gray in terms of $k$-symmetric spaces. In this case, a $k$-manifold is an homogeneous reductive space and the classification of these varieties is given by the corresponding classification of graded Lie algebras. The general notion of a $\\Gamma $-symmetric space was introduced by R.Lutz. We approach the classification of such spaces in the case $\\Gamma=Z_2^2$ using recent results on the classification of complex $Z_2^2$-graded simple Lie algebras.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-02-09T09:20:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C30",
      "53C35",
      "17B20"
    ],
    "keywords": [
      "symmetric space",
      "classification",
      "general finite abelian group",
      "graded simple lie algebras",
      "algebraic point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....12098B"
    }
  }
}