{
  "id": "1811.09948",
  "version": "v1",
  "published": "2018-11-25T05:43:50.000Z",
  "updated": "2018-11-25T05:43:50.000Z",
  "title": "The Automorphisms group of a Current Lie algebra",
  "authors": [
    "Jesús Alonso Ochoa Arango",
    "Nadina Elizabeth Rojas"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT",
    "math.AC",
    "math.RA"
  ],
  "abstract": "Let $\\mathfrak{g}$ be a finite dimensional complex Lie algebra and let $A$ be a finite dimensional complex, associative and commutative algebra with unit. We describe the structure of the derivation Lie algebra of the current Lie algebra $\\mathfrak{g}_A= \\mathfrak{g} \\otimes A$, denoted by $\\operatorname{Der}(\\mathfrak{g}_A)$. Furthermore, we obtain the Levi decomposition of $\\operatorname{Der}(\\mathfrak{g}_A)$. As a consequence of the last result, if $\\mathfrak{h}_m$ is the Heisenberg Lie algebra of dimension $2 m + 1$, we obtain a faithful representation of $\\operatorname{Der}(\\mathfrak{h}_{m,k})$ of the current truncated Heisenberg Lie algebra $\\mathfrak{h}_{m,k}= \\mathfrak{h}_m \\otimes \\mathbb{C}[t]/ (t^{k + 1})$ for all positive integer $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-25T05:43:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B30",
      "17B40",
      "17B45"
    ],
    "keywords": [
      "current lie algebra",
      "automorphisms group",
      "finite dimensional complex lie algebra",
      "current truncated heisenberg lie algebra",
      "derivation lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}