{
  "id": "1405.4035",
  "version": "v2",
  "published": "2014-05-15T23:30:41.000Z",
  "updated": "2014-07-07T16:10:25.000Z",
  "title": "Universal central extensions of $\\mathfrak{sl}(m, n, A)$ of small rank over associative superalgebras",
  "authors": [
    "Xabier García-Martínez",
    "Manuel Ladra"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We complete the solution of the problem of finding the universal central extension of the matrix superalgebras $\\mathfrak{sl}(m, n, A)$ where $A$ is an associative superalgebra and computing $H_2\\big(\\mathfrak{sl}(m, n, A)\\big)$. The Steinberg Lie superalgebra $\\mathfrak{st}(m, n, A)$ has a very important role and we will also find out $H_2\\big(\\mathfrak{st}(m, n, A)\\big)$. In Chen and Sun (arXiv:1311.7079, 2013) it is solved the problem where $m+n \\geq 5$ and in Chen and Guay (Algebr. Represent. Theory, 2013) it is solved when $n=0$, so here we work out the three remaining cases $\\mathfrak{sl}(2, 1, A), \\mathfrak{sl}(3, 1, A)$ and $\\mathfrak{sl}(2, 2, A)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-07-07T16:10:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B60",
      "17B55",
      "17B05"
    ],
    "keywords": [
      "universal central extension",
      "associative superalgebra",
      "small rank",
      "steinberg lie superalgebra",
      "matrix superalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.4035G"
    }
  }
}