{
  "id": "2303.12508",
  "version": "v1",
  "published": "2023-03-22T12:30:19.000Z",
  "updated": "2023-03-22T12:30:19.000Z",
  "title": "Classification of orbit closures in the variety of 4-dimensional symplectic Lie algebras",
  "authors": [
    "Edison Alberto Fernández-Culma",
    "Nadina Elizabeth Rojas"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "The aim of this paper is to study the natural action of the real symplectic group, $\\operatorname{Sp}(4, \\mathbb{R})$, on the algebraic set of $4$-dimensional Lie algebras admitting symplectic structures and to give a complete classification of orbit closures. We present some applications of such classification to the study of the Ricci curvature of left-invariant almost K\\\"{a}hler structures on four dimensional Lie groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-22T12:30:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic lie algebras",
      "orbit closures",
      "classification",
      "lie algebras admitting symplectic structures",
      "dimensional lie algebras admitting symplectic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}