{
  "id": "2302.04251",
  "version": "v1",
  "published": "2023-02-08T18:35:46.000Z",
  "updated": "2023-02-08T18:35:46.000Z",
  "title": "Definability of Lie isomorphisms of groups definable in o-minimal expansions of the real field",
  "authors": [
    "Alf Onshuus"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this paper, we study the relation between the category of real Lie groups and that of groups definable in o-minimal expansions of the real field (which we will refer to as ``definable groups''). It is known (\\cite{Pi88}) that any group definable in an o-minimal expansion of the real field is a Lie group, and in \\cite{COP} a complete characterization of when a Lie group has a ``definable group'' which is Lie isomorphic to it was given. In this paper we continue the analysis by explaining when a Lie homomorphism between definable groups is a definable isomorphism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-08T18:35:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real field",
      "o-minimal expansion",
      "lie isomorphisms",
      "groups definable",
      "definable group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}