{
  "id": "2202.07985",
  "version": "v1",
  "published": "2022-02-16T10:55:11.000Z",
  "updated": "2022-02-16T10:55:11.000Z",
  "title": "Irreducible Integrable Modules for the full Toroidal Lie Algebras co-ordinated by Rational Quantum Torus",
  "authors": [
    "Santanu Tantubay",
    "Punita Batra"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathbb{C}_q$ be a non-commutative Laurent polynomial ring associated with a $(n+1)\\times (n+1)$ rational quantum matrix $q$. Let $\\mathfrak{sl}_d(\\mathbb{C}_q)\\oplus HC_1(\\mathbb{C}_q)$ be the universal central extension of Lie subalgebra $\\mathfrak{sl}_d(\\mathbb{C}_q)$ of $\\mathfrak{gl}_d(\\mathbb{C}_q)$. Now let us take the Lie algebra $\\tau=\\mathfrak{gl}_d(\\mathbb{C}_q)\\oplus HC_1(\\mathbb{C}_q)$. Let $Der(\\mathbb{C}_q)$ be the Lie algebra of all derivations of $\\mathbb{C}_q$. Now we consider the Lie algebra $\\tilde{\\tau}=\\tau\\rtimes Der(\\mathbb{C}_q)$, called as full toroidal Lie algebra co-ordinated by rational quantum tori. In this paper we get a classification of irreducible integrable modules with finite dimensional weight spaces for $\\tilde{\\tau}$ with nonzero central action on the modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-16T10:55:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B65",
      "17B66"
    ],
    "keywords": [
      "full toroidal lie algebra",
      "rational quantum torus",
      "irreducible integrable modules",
      "laurent polynomial ring",
      "finite dimensional weight spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}