{
  "id": "1607.07067",
  "version": "v1",
  "published": "2016-07-24T17:03:39.000Z",
  "updated": "2016-07-24T17:03:39.000Z",
  "title": "Classification of Category $\\mathcal{J}$ Modules for Divergence Zero Vector Fields on a Torus",
  "authors": [
    "Yuly Billig",
    "John Talboom"
  ],
  "comment": "15 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "A family of modules for the Lie algebra of vector fields on a torus, called category $\\mathcal{J}$, is defined in [1] where indecomposable modules in this category are classified. Modules in category $\\mathcal{J}$ are required to admit an action by the algebra of Laurent polynomials that is compatible with that of the Lie algebra of vector fields. This paper presents an analogous category $\\mathcal{J}$ for the subalgebra of divergence zero vector fields on a torus and classifies the indecomposable modules of this category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-07-24T17:03:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B66"
    ],
    "keywords": [
      "divergence zero vector fields",
      "classification",
      "lie algebra",
      "indecomposable modules",
      "laurent polynomials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}