{
  "id": "1309.7544",
  "version": "v3",
  "published": "2013-09-29T07:01:10.000Z",
  "updated": "2015-01-28T12:10:12.000Z",
  "title": "The irreducible modules for the derivations of the rational quantum torus",
  "authors": [
    "S. Eswara Rao",
    "Punita Batra",
    "Sachin S. Sharma"
  ],
  "comment": "Revised version",
  "journal": "J.Algebra 410(2014), 333-342",
  "doi": "10.1016/j.jalgebra.2014.03.024",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\bbcq$ be the quantum torus associated with the $d \\times d$ matrix $q = (q_{ij})$, $q_{ii} = 1$, $q_{ij}^{-1} = q_{ji}$, $q_{ij}$ are roots of unity, for all $1 \\leq i, j \\leq d.$ Let $\\Der(\\bbcq)$ be the Lie algebra of all the derivations of $\\bbcq$. In this paper we define the Lie algebra $\\Der(\\bbcq) \\ltimes \\bbcq$ and classify its modules which are irreducible and have finite dimensional weight spaces. These modules under certain conditions turn out to be of the form $V \\otimes \\bbcq$, where $V$ is a finite dimensional irreducible $gl_d$-module.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-10-01T06:03:21.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-01-28T12:10:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B66",
      "17B68"
    ],
    "keywords": [
      "rational quantum torus",
      "irreducible modules",
      "derivations",
      "finite dimensional weight spaces",
      "lie algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.7544E"
    }
  }
}