{
  "id": "1703.04948",
  "version": "v1",
  "published": "2017-03-15T06:08:13.000Z",
  "updated": "2017-03-15T06:08:13.000Z",
  "title": "Complete classification of pseudo $H$-type algebras: II",
  "authors": [
    "Kenro Furutani",
    "Irina Markina"
  ],
  "comment": "29 pages, 7 tables",
  "categories": [
    "math.RT"
  ],
  "abstract": "We classify a class of 2-step nilpotent Lie algebras related to the representations of the Clifford algebras in the following way. Let $J\\colon \\Cl(\\mathbb R^{r,s})\\toU$ be a representation of the Clifford algebra $\\Cl(\\mathbb R^{r,s})$ generated by the pseudo Euclidean vector space $\\mathbb R^{r,s}$. Assume that the Clifford module $U$ is endowed with a bilinear symmetric non-degenerate real form $\\la\\cdot\\,,\\cdot\\ra_U$ making the linear map $J_z$ skew symmetric for any $z\\in\\mathbb R^{r,s}$. The Lie algebras and the Clifford algebras are related by $\\la J_zv,w\\ra_U=\\la z,[v,w]\\ra_{\\mathbb R^{r,s}}$, $z\\in \\mathbb R^{r,s}$, $v,w\\in U$. We detect the isomorphic and non-isomorphic Lie algebras according to the dimension of $U$ and the range of the non-negative integers~$r,s$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-15T06:08:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complete classification",
      "type algebras",
      "clifford algebra",
      "bilinear symmetric non-degenerate real form",
      "pseudo euclidean vector space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}