{
  "id": "math-ph/0110007",
  "version": "v3",
  "published": "2001-10-03T16:50:04.000Z",
  "updated": "2001-12-25T17:53:24.000Z",
  "title": "Quantum de Rham complex with $d^3 = 0$ differential",
  "authors": [
    "N. Bazunova",
    "A. Borowiec",
    "R. Kerner"
  ],
  "comment": "6 pages, submitted to Czechoslovak Journal of Physics v. 51 (2001)",
  "journal": "Czech. J. Phys., 51 2001 1266",
  "doi": "10.1023/A:1013301532095",
  "categories": [
    "math-ph",
    "math.MP",
    "math.QA"
  ],
  "abstract": "In this work, we construct the de Rham complex with differential operator d satisfying the Q-Leibniz rule, where Q is a complex number, and the condition $d^3=0$ on an associative unital algebra with quadratic relations. Therefore we introduce the second order differentials $d^2x^i$. In our formalism, besides the usual two-dimensional quantum plane, we observe that the second order differentials $d^2 x$ and $d^2 y$ generate either bosonic or fermionic quantum planes, depending on the choice of the differentiation parameter Q.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2001-12-25T17:53:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37"
    ],
    "keywords": [
      "rham complex",
      "second order differentials",
      "usual two-dimensional quantum plane",
      "fermionic quantum planes",
      "differential operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}