{
  "id": "0812.4158",
  "version": "v6",
  "published": "2008-12-22T11:39:10.000Z",
  "updated": "2014-06-30T10:28:00.000Z",
  "title": "On Borel complexity of the isomorphism problems for graph-related classes of Lie algebras and finite p-groups",
  "authors": [
    "Ruvim Lipyanski",
    "Natalia Vanetik"
  ],
  "comment": "14 pages, no figures",
  "categories": [
    "math.GR",
    "math.CO",
    "math.RA"
  ],
  "abstract": "We reduce the isomorphism problem for undirected graphs without loops to the isomorphism problems for a class of finite dimensional $2$-step nilpotent Lie algebras over a field and for a class of finite $p$-groups. We show that the isomorphism problem for graphs is harder than the two latter isomorphism problems in the sense of Borel reducibility. A computable analogue of Borel reducibility was introduced by S. Coskey, J.D. Hamkins, and R. Miller. A relation of the isomorphism problem for undirected graphs to the well-known problem of classifying pairs of matrices over a field (up to similarity) is also studied.",
  "revisions": [
    {
      "version": "v6",
      "updated": "2014-06-30T10:28:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20D15"
    ],
    "keywords": [
      "isomorphism problem",
      "borel complexity",
      "finite p-groups",
      "graph-related classes",
      "borel reducibility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.4158L"
    }
  }
}