{
  "id": "2012.01003",
  "version": "v1",
  "published": "2020-12-02T07:41:30.000Z",
  "updated": "2020-12-02T07:41:30.000Z",
  "title": "Categories $\\mathcal{O}$ for Root-Reductive Lie Algebras: II. Translation Functors and Tilting Modules",
  "authors": [
    "Thanasin Nampaisarn"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "This is the second paper of a series of papers on a version of categories $\\mathcal{O}$ for root-reductive Lie algebras. Let $\\mathfrak{g}$ be a root-reductive Lie algebra over an algebraically closed field $\\mathbb{K}$ of characteristic $0$ with a splitting Borel subalgebra $\\mathfrak{b}$ containing a splitting maximal toral subalgebra $\\mathfrak{h}$. For some pairs of blocks $\\overline{\\mathcal{O}}[\\lambda]$ and $\\overline{\\mathcal{O}}[\\mu]$, the subcategories whose objects have finite length are equivalence via functors obtained by the direct limits of translation functors. Tilting objects can also be defined in $\\overline{\\mathcal{O}}$. There are also universal tilting objects $D(\\lambda)$ in parallel to the finite-dimensional cases.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-02T07:41:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B20",
      "17B22",
      "17B65"
    ],
    "keywords": [
      "root-reductive lie algebra",
      "translation functors",
      "tilting modules",
      "categories",
      "splitting maximal toral subalgebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}