{
  "id": "1412.6801",
  "version": "v1",
  "published": "2014-12-21T15:50:29.000Z",
  "updated": "2014-12-21T15:50:29.000Z",
  "title": "Finite W-superalgebras for basic Lie superalgebras",
  "authors": [
    "Yang Zeng",
    "Bin Shu"
  ],
  "comment": "42 pages. This version is revised from the first 6 chapters of the manuscript \"Finite W-superalgebras for basic classical Lie superalgebras\" (arXiv:1404.1150 [math.RT])",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We consider the finite $W$-superalgebra $U(\\mathfrak{g_\\bbf},e)$ for a basic Lie superalgebra ${\\ggg}_\\bbf=(\\ggg_\\bbf)_\\bz+(\\ggg_\\bbf)_\\bo$ associated with a nilpotent element $e\\in (\\ggg_\\bbf)_{\\bar0}$ both over the field of complex numbers $\\bbf=\\mathbb{C}$ and over $\\bbf={\\bbk}$ an algebraically closed field of positive characteristic. In this paper, we mainly present the PBW theorem for $U({\\ggg}_\\bbf,e)$. Then the construction of $U({\\ggg}_\\bbf,e)$ can be understood well, which in contrast with finite $W$-algebras, is divided into two cases in virtue of the parity of $\\text{dim}\\,\\mathfrak{g_\\bbf}(-1)_{\\bar1}$. This observation will be a basis of our sequent work on the dimensional lower bounds in the super Kac-Weisfeiler property of modular representations of basic Lie superalgebras (cf. \\cite[\\S7-\\S9]{ZS}).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-21T15:50:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "basic lie superalgebra",
      "finite w-superalgebras",
      "dimensional lower bounds",
      "super kac-weisfeiler property",
      "pbw theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1335871
    }
  }
}