{
  "id": "1603.00373",
  "version": "v1",
  "published": "2016-03-01T17:35:36.000Z",
  "updated": "2016-03-01T17:35:36.000Z",
  "title": "Rigidity of 2-step Carnot groups",
  "authors": [
    "Mauricio Godoy Molina",
    "Boris Kruglikov",
    "Irina Markina",
    "Alexander Vasil'ev"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.DG"
  ],
  "abstract": "In the present paper we study the rigidity of 2-step Carnot groups, or equivalently, of graded 2-step nilpotent Lie algebras. We prove the alternative that depending on bi-dimensions of the algebra, the Lie algebra structure makes it either always of infinite type or generically rigid, and we specify the bi-dimensions for each of the choices. Explicit criteria for rigidity of pseudo $H$- and $J$-type algebras are given. In particular, we establish the relation of the so-called $J^2$-condition to rigidity, and we explore these conditions in relation to pseudo $H$-type algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-01T17:35:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B30",
      "17B70",
      "16W55",
      "22E60"
    ],
    "keywords": [
      "carnot groups",
      "type algebras",
      "nilpotent lie algebras",
      "lie algebra structure",
      "bi-dimensions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1441136
    }
  }
}