{
  "id": "1206.5867",
  "version": "v2",
  "published": "2012-06-26T00:55:42.000Z",
  "updated": "2012-11-15T15:18:04.000Z",
  "title": "Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor",
  "authors": [
    "Nadina Elizabeth Rojas"
  ],
  "comment": "8 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "For a finite dimensional Lie algebra $\\g$ over a field $\\k$ of characteristic zero, the $\\mu$-function (respectively $\\mu_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\\g$ admits a faithful representation (respectively a faithful nilrepresentation) on $V$. Let $\\h_m$ be the Heisenberg Lie algebra of dimension $2m + 1$ and let $\\mathfrak{a}_n$ be the abelian Lie algebra of dimension $n$. The aim of this paper is to compute $\\mu(\\h_m \\oplus \\mathfrak{a}_n)$ and $\\mu_{nil}(\\h_m \\oplus \\mathfrak{a}_n)$ for all $m,n \\in \\mathbb{N}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-11-15T15:18:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B30",
      "20C40"
    ],
    "keywords": [
      "heisenberg lie algebra",
      "minimal faithful representation",
      "abelian factor",
      "finite dimensional lie algebra",
      "abelian lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1206.5867R"
    }
  }
}