{
  "id": "0807.4811",
  "version": "v1",
  "published": "2008-07-30T09:17:59.000Z",
  "updated": "2008-07-30T09:17:59.000Z",
  "title": "Deforming the Lie Superalgebra $\\mathcal{K}(1)$-Modules Of Symbols",
  "authors": [
    "Ammar Faouzi",
    "Kamoun Kaouthar"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability of infinitesimal multi-parameter deformation and determine the complete commutative algebra corresponding to the miniversal deformation in the sense of A. Fialowski. Besides, we compute the first even differential cohomology space $mathrmH^1_{mathrm{diff}}(cK(1);widetilde{cD}_{lambda,mu})$ of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ with coefficients in the superspace $widetilde{mathcalD}_{lambda,mu}$ of linear differential operators from the superspace of weighted densities $\\fF_{\\lamda}$ to $\\fF_{\\mu}$. (To appear in Journal of Generalized Lie Theory and Applications)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-07-30T09:17:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lie superalgebra",
      "contact vector fields",
      "superspace",
      "linear differential operators",
      "infinitesimal multi-parameter deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.4811F"
    }
  }
}