{
  "id": "1805.02057",
  "version": "v1",
  "published": "2018-05-05T13:54:21.000Z",
  "updated": "2018-05-05T13:54:21.000Z",
  "title": "Abelian ideals of a Borel subalgebra and root systems, II",
  "authors": [
    "Dmitri I. Panyushev"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Let $\\mathfrak g$ be a simple Lie algebra with a Borel subalgebra $\\mathfrak b$ and $\\mathfrak{Ab}$ the set of abelian ideals of $\\mathfrak b$. Let $\\Delta^+$ be the corresponding set of positive roots. We continue our study of combinatorial properties of the partition of $\\mathfrak{Ab}$ parameterised by the long positive roots. In particular, the union of an arbitrary set of maximal abelian ideals is described, if $\\mathfrak g\\ne\\mathfrak{sl}_n$. We also characterise the greatest lower bound of two positive roots, when it exists, and point out interesting subposets of $\\Delta^+$ that are modular lattices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-05T13:54:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B20",
      "17B22",
      "06A07",
      "20F55"
    ],
    "keywords": [
      "borel subalgebra",
      "root systems",
      "maximal abelian ideals",
      "greatest lower bound",
      "simple lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}