{
  "id": "1802.02112",
  "version": "v1",
  "published": "2018-02-06T18:19:41.000Z",
  "updated": "2018-02-06T18:19:41.000Z",
  "title": "Projective modules over classical Lie algebras of infinite rank in the parabolic category",
  "authors": [
    "Chih-Whi Chen",
    "Ngau Lam"
  ],
  "comment": "27 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the truncation functors and show the existence of projective cover of each irreducible module in parabolic BGG category $\\mathcal O$ over infinite rank Lie algebra of types $\\mathfrak{a,b,c,d}$. Moreover, $\\mathcal O$ is a Koszul category. As a consequence, the corresponding parabolic BGG category $\\overline{\\mathcal O}$ over infinite rank Lie superalgebra of types $\\mathfrak{a,b,c,d}$ through the super duality is also a Koszul category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T18:19:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10"
    ],
    "keywords": [
      "classical lie algebras",
      "parabolic category",
      "projective modules",
      "infinite rank lie algebra",
      "koszul category"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}