{
  "id": "0811.2073",
  "version": "v2",
  "published": "2008-11-13T11:22:43.000Z",
  "updated": "2009-10-19T18:35:59.000Z",
  "title": "Functoriality of the BGG Category O",
  "authors": [
    "Apoorva Khare"
  ],
  "comment": "Final form of a much expanded, improved, and generalized version of a previous preprint - arXiv:math/0504371. Accepted for publication in Communications in Algebra; 45 pages, laTeX",
  "journal": "Communications in Algebra 37 (2009), no. 12, 4431-4475",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category O. We study functorial properties of O across various setups. The first setup is over a skew group ring, involving a finite group $\\Gamma$ acting on a regular triangular algebra $A$. We develop Clifford theory for $A \\rtimes \\Gamma$, and obtain results on block decomposition, complete reducibility, and enough projectives. O is shown to be a highest weight category when $A$ satisfies one of the \"Conditions (S)\"; the BGG Reciprocity formula is slightly different because the duality functor need not preserve each simple module. Next, we turn to tensor products of such skew group rings; such a product is also a skew group ring. We are thus able to relate four different types of Categories O; more precisely, we list several conditions, each of which is equivalent in any one setup, to any other setup - and which yield information about O.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-10-19T18:35:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16D90",
      "16S35"
    ],
    "keywords": [
      "bgg category",
      "skew group ring",
      "functoriality",
      "study functorial properties",
      "regular triangular algebra"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0811.2073K"
    }
  }
}