{
  "id": "1802.01814",
  "version": "v1",
  "published": "2018-02-06T06:30:38.000Z",
  "updated": "2018-02-06T06:30:38.000Z",
  "title": "Non-weight modules over algebras related to the Virasoro algebra",
  "authors": [
    "Qiu-Fan Chen",
    "Yu-Feng Yao"
  ],
  "comment": "14 pages. Comments are welcome",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper, we study a class of non-weight modules over two kinds of algebras related to the Virasoro algebra, i.e., the loop-Virasoro algebras $\\mathfrak{L}$ and a class of Block type Lie algebras $\\mathfrak{B(q)}$, where $q$ is a nonzero complex number. We determine those modules whose restriction to the Cartan subalgebra (modulo center) are free of rank one. We also provide a sufficient and necessary condition for such modules to be simple, and determine their isomorphism classes. Moreover, we obtain the simplicity of modules over loop-Virasoro algebras by taking tensor products of some irreducible modules mentioned above with irreducible highest weight modules or Whittaker modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T06:30:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-weight modules",
      "block type lie algebras",
      "loop-virasoro algebras",
      "irreducible highest weight modules",
      "nonzero complex number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}