{
  "id": "1709.10334",
  "version": "v1",
  "published": "2017-09-29T11:23:53.000Z",
  "updated": "2017-09-29T11:23:53.000Z",
  "title": "Wildness of the problems of classifying two-dimensional spaces of commuting linear operators and certain Lie algebras",
  "authors": [
    "Vyacheslav Futorny",
    "Tetiana Klymchuk",
    "Anatolii P. Petravchuk",
    "Vladimir V. Sergeichuk"
  ],
  "comment": "11 pages",
  "journal": "Linear Algebra and Its Applications 536 (2018) 201-209",
  "doi": "10.1016/j.laa.2017.09.019",
  "categories": [
    "math.RT"
  ],
  "abstract": "For each two-dimensional vector space $V$ of commuting $n\\times n$ matrices over a field $\\mathbb F$ with at least 3 elements, we denote by $\\widetilde V$ the vector space of all $(n+1)\\times(n+1)$ matrices of the form $\\left[\\begin{smallmatrix}A&*\\\\0&0\\end{smallmatrix}\\right]$ with $A\\in V$. We prove the wildness of the problem of classifying Lie algebras $\\widetilde V$ with the bracket operation $[u,v]:=uv-vu$. We also prove the wildness of the problem of classifying two-dimensional vector spaces consisting of commuting linear operators on a vector space over a field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-09-29T11:23:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A21",
      "16G60",
      "17B10"
    ],
    "keywords": [
      "commuting linear operators",
      "classifying two-dimensional spaces",
      "lie algebras",
      "classifying two-dimensional vector spaces consisting"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}