{
  "id": "1212.1404",
  "version": "v2",
  "published": "2012-12-06T18:13:50.000Z",
  "updated": "2013-04-09T03:05:38.000Z",
  "title": "A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules",
  "authors": [
    "Georgia Benkart",
    "Samuel A. Lopes",
    "Matthew Ondrus"
  ],
  "comment": "30 pages, a few of the sections have been placed in a different order at the suggestion of the referee",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "An Ore extension over a polynomial algebra F[x] is either a quantum plane, a quantum Weyl algebra, or an infinite-dimensional unital associative algebra A_h generated by elements x,y, which satisfy yx-xy = h, where h is in F[x]. When h is nonzero, these algebras are subalgebras of the Weyl algebra A_1 and can be viewed as differential operators with polynomial coefficients. In previous work, we studied the structure of A_h and determined its automorphism group and the subalgebra of invariants under the automorphism group. Here we determine the irreducible A_h-modules. In a sequel to this paper, we completely describe the derivations of A_h over any field.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-04-09T03:05:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16S32",
      "16D60",
      "05E15"
    ],
    "keywords": [
      "irreducible modules",
      "subalgebra",
      "parametric family",
      "automorphism group",
      "quantum weyl algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.1404B"
    }
  }
}