{
  "id": "math/0310180",
  "version": "v1",
  "published": "2003-10-13T12:08:09.000Z",
  "updated": "2003-10-13T12:08:09.000Z",
  "title": "Classification of four-dimensional Lie algebras admitting a para-hypercomplex structure",
  "authors": [
    "N. Blazic",
    "S. Vukmirovic"
  ],
  "comment": "15 pages",
  "categories": [
    "math.DG"
  ],
  "abstract": "The main goal is to classify 4-dimensional real Lie algebras $\\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore possessing a neutral, left-invariant, anti-self-dual metric. Our study is related to the work of Barberis who classified real, 4-dimensional simply-connected Lie groups which admit an invariant hypercomplex structure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-10-13T12:08:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C50",
      "53C56",
      "32M10",
      "53C26",
      "53C55"
    ],
    "keywords": [
      "four-dimensional lie algebras admitting",
      "para-hypercomplex structure",
      "classification",
      "lie groups",
      "invariant hypercomplex structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10180B"
    }
  }
}