{
  "id": "1401.0755",
  "version": "v1",
  "published": "2014-01-04T00:01:45.000Z",
  "updated": "2014-01-04T00:01:45.000Z",
  "title": "Centers associated with the Borel subalgebra of the general linear Lie algebra",
  "authors": [
    "Oz Ben-Shimol"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We consider a Borel subalgebra $\\fg$ of the general linear algebra and its subalgebra $\\BB$ which is a Borel subalgebra of the special linear algebra, over arbitrary field. Let $\\cL\\in\\{\\fg, \\BB\\}$. We establish here explicit realizations of the center $Z(\\cL)$ and semi-center $Sz(\\cL)$ of the enveloping algebra, the Poisson center $S(\\cL)^{\\cL}$ and Poisson semi-center $S(\\cL)^{\\cL}_{\\si}$ of the symmetric algebra. We describe their structure as commutative rings and establish isomorphisms $Z(\\cL)\\cong S(\\cL)^{\\cL}$, $Sz(\\cL)\\cong S(\\cL)^{\\cL}_{\\si}$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-01-04T00:01:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general linear lie algebra",
      "borel subalgebra",
      "special linear algebra",
      "general linear algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1401.0755B"
    }
  }
}