{
  "id": "1304.6003",
  "version": "v2",
  "published": "2013-04-22T16:12:51.000Z",
  "updated": "2013-05-06T13:56:26.000Z",
  "title": "Poisson and Hochschild cohomology and the semiclassical limit",
  "authors": [
    "Matthew Towers"
  ],
  "comment": "Comments to m.towers@kent.ac.uk welcome",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "Let $B$ be a quantum algebra possessing a semiclassical limit $A$. We show that under certain hypotheses $B^e$ can be thought of as a deformation of the Poisson enveloping algebra of $A$, and we give a criterion for the Hochschild cohomology of $B$ to be a deformation of the Poisson cohomology of $A$ in the case that $B$ is Koszul. We verify that condition for the algebra of $2\\times 2$ quantum matrices and calculate its Hochschild cohomology and the Poisson cohomology of its semiclassical limit.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-05-06T13:56:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40",
      "17B63",
      "20G42"
    ],
    "keywords": [
      "hochschild cohomology",
      "semiclassical limit",
      "poisson cohomology",
      "quantum matrices",
      "deformation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.6003T"
    }
  }
}