{
  "id": "2105.00536",
  "version": "v1",
  "published": "2021-05-02T19:16:33.000Z",
  "updated": "2021-05-02T19:16:33.000Z",
  "title": "Representation of Real Solvable Lie Algebras Having 2-dimensional Derived Ideal",
  "authors": [
    "Tu T. C Nguyen",
    "Vu A. Le"
  ],
  "comment": "24 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Given a Lie algebra $\\mathcal{G}$, let $\\mu(\\mathcal{G})$ be the minimal degree of a faithful representation of $\\mathcal{G}$. This is an integer valued invariant of $\\mathcal{G}$, which has been introduced by D. Burde in 1998. In general it is not known how to determine this invariant. In particular, this seems to be very hard for a given solvable Lie algebra. Lie($n,k$) denotes the class of all $n$-dimensional real solvable Lie algebras having $k$-dimensional derived ideals. In 2020, we gave a classification of all non 2-step nilpotent Lie algebras of Lie($n$,2). In this paper, we give an upper bound of $\\mu(\\mathcal{G})$ for each $\\mathcal{G}$ classified. For indecomposable case, we further compute the characters afforded by the adjoint, coadjoint representations and describe the picture of coadjoint orbits of Lie groups corresponding to them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-02T19:16:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B08"
    ],
    "keywords": [
      "representation",
      "dimensional real solvable lie algebras",
      "nilpotent lie algebras",
      "integer valued invariant",
      "upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}