{
  "id": "0803.1076",
  "version": "v1",
  "published": "2008-03-07T12:32:25.000Z",
  "updated": "2008-03-07T12:32:25.000Z",
  "title": "Faithful representations of minimal dimension of current Heisenberg Lie algebras",
  "authors": [
    "L. Cagliero",
    "N. Rojas"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Given a Lie algebra $\\mathfrak{g}$ over a field of characteristic zero $k$, let $\\mu(\\mathfrak{g})=\\min\\{\\dim \\pi: \\pi\\text{is a faithful representation of}\\mathfrak{g}\\}$. Let $\\mathfrak{h}_{m}$ be the Heisenberg Lie algebra of dimension $2m+1$ over $k$ and let $k[t]$ be the polynomial algebra in one variable. Given $m\\in\\mathbb{N}$ and $p\\in k[t]$, let $\\mathfrak{h}_{m,p}=\\mathfrak{h}_m\\otimes k[t]/(p)$ be the current Lie algebra associated to $\\mathfrak{h}_m$ and $k[t]/(p)$, where $(p)$ is the principal ideal in $k[t]$ generated by $p$. In this paper we prove that $ mu(\\mathfrak{h}_{m,p}) = m \\deg p + \\left \\lceil 2\\sqrt{\\deg p} \\right\\rceil$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-07T12:32:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B30"
    ],
    "keywords": [
      "current heisenberg lie algebras",
      "minimal dimension",
      "faithful representations",
      "polynomial algebra",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1076C"
    }
  }
}