{
  "id": "1802.06343",
  "version": "v1",
  "published": "2018-02-18T07:37:21.000Z",
  "updated": "2018-02-18T07:37:21.000Z",
  "title": "On an infinite limit of BGG categories O",
  "authors": [
    "Kevin Coulembier",
    "Ivan Penkov"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study a version of the BGG category O for Dynkin Borel subalgebras of root-reductive Lie algebras, such as g=gl(infinity). We prove results about extension fullness and compute the higher extensions of simple modules by Verma modules. We also show that the category is Ringel self-dual and initiate the study of Koszul duality. An important tool in obtaining these results is an equivalence we establish between appropriate Serre subquotients of category O for g and category O for finite dimensional reductive subalgebras of g.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-18T07:37:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bgg category",
      "infinite limit",
      "finite dimensional reductive subalgebras",
      "dynkin borel subalgebras",
      "appropriate serre subquotients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}