{
  "id": "1711.11234",
  "version": "v1",
  "published": "2017-11-30T05:21:34.000Z",
  "updated": "2017-11-30T05:21:34.000Z",
  "title": "On Categories $\\mathcal{O}$ for Root-Reductive Lie Algebras",
  "authors": [
    "Thanasin Nampaisarn"
  ],
  "comment": "33 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "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 $\\mathfrak{h}$. We study the category $\\bar{\\mathcal{O}}$ consisting of all $\\mathfrak{h}$-weight $\\mathfrak{g}$-modules which are locally $\\mathfrak{b}$-finite and have finite-dimensional $\\mathfrak{h}$-weight spaces. The focus is on very special Borel subalgebras called the Dynkin Borel subalgebras. This paper serves as an initial passage to the understanding of categories $\\mathcal{O}$ for infinite-dimensional root-reductive Lie algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-30T05:21:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B22",
      "17B65"
    ],
    "keywords": [
      "dynkin borel subalgebras",
      "splitting maximal toral subalgebra",
      "special borel subalgebras",
      "infinite-dimensional root-reductive lie algebras",
      "weight spaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}