{
  "id": "quant-ph/0510106",
  "version": "v3",
  "published": "2005-10-13T20:29:00.000Z",
  "updated": "2007-09-20T14:43:54.000Z",
  "title": "Fine grading of $sl(p^2,\\mathbb{C})$ generated by tensor product of generalized Pauli matrices and its symmetries",
  "authors": [
    "Edita Pelantova",
    "Milena Svobodova",
    "Sébastien Tremblay"
  ],
  "journal": "Journal of Mathematical Physics, 2006, 47, No 1, 5341-5357",
  "doi": "10.1063/1.2162149",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Study of the normalizer of the MAD-group corresponding to a finegrading offers the most important tool for describing symmetries in the system of non-linear equations connected with contraction of a Lie algebra. One fine grading that is always present in any Lie algebra $sl(n,\\mathbb{C})$ is the Pauli grading. The MAD-group corresponding to it is generated by generalized Pauli matrices. For such MAD-group, we already know its normalizer; its quotient group is isomorphic to the Lie group $Sl(2,\\mathbb{Z}_n)\\times v\\mathbb{Z}_2$. In this paper, we deal with a more complicated situation, namely that the fine grading of $sl(p^2, \\mathbb{C})$ is given by a tensor product of the Pauli matrices of the same order $p$, $p$ being a prime. We describe the normalizer of the corresponding MAD-group and we show that its quotient group is isomorphic to $Sp(4,\\mathbb{Z}_p)\\times\\mathbb{Z}_2$.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2007-09-20T14:43:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized pauli matrices",
      "tensor product",
      "fine grading",
      "symmetries",
      "quotient group"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "AIP",
      "journal": "J. Math. Phys."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}