{
  "id": "math-ph/0506044",
  "version": "v1",
  "published": "2005-06-16T14:50:54.000Z",
  "updated": "2005-06-16T14:50:54.000Z",
  "title": "Symmetries of modules of differential operators",
  "authors": [
    "Hichem Gargoubi",
    "Pierre Mathonet",
    "Valentin Ovsienko"
  ],
  "comment": "29 pages, LaTeX, 4 figures",
  "journal": "Journal of Nonlinear Mathematical Physics 12 (2005) 348-380",
  "categories": [
    "math-ph",
    "math.DG",
    "math.MP"
  ],
  "abstract": "Let ${\\cal F}\\_\\lambda(S^1)$ be the space of tensor densities of degree (or weight) $\\lambda$ on the circle $S^1$. The space ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$ of $k$-th order linear differential operators from ${\\cal F}\\_\\lambda(S^1)$ to ${\\cal F}\\_\\mu(S^1)$ is a natural module over $\\mathrm{Diff}(S^1)$, the diffeomorphism group of $S^1$. We determine the algebra of symmetries of the modules ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$, i.e., the linear maps on ${\\cal D}^k\\_{\\lambda,\\mu}(S^1)$ commuting with the $\\mathrm{Diff}(S^1)$-action. We also solve the same problem in the case of straight line $\\mathbb{R}$ (instead of $S^1$) and compare the results in the compact and non-compact cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-06-16T14:50:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B56"
    ],
    "keywords": [
      "symmetries",
      "th order linear differential operators",
      "diffeomorphism group",
      "linear maps",
      "tensor densities"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.2991/jnmp.2005.12.3.4",
      "journal": "Journal of Nonlinear Mathematical Physics",
      "year": 2005,
      "volume": 12,
      "number": 3,
      "pages": 348
    },
    "note": {
      "typesetting": "LaTeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005JNMP...12..348G"
    }
  }
}