{
  "id": "2304.13475",
  "version": "v1",
  "published": "2023-04-26T11:59:04.000Z",
  "updated": "2023-04-26T11:59:04.000Z",
  "title": "On solubility of skew left braces and solutions of the Yang-Baxter equation",
  "authors": [
    "Adolfo Ballester-Bolinches",
    "Ramón Esteban-Romero",
    "Paz Jiménez-Seral",
    "Vicent Pérez-Calabuig"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR",
    "math.RA"
  ],
  "abstract": "The study of non-degenerate set-theoretic solutions of the Yang-Baxter equation calls for a deep understanding of the algebraic structure of a skew left brace. In this paper, we describe finite skew left braces admitting no proper substructure, we introduce a suitable notion of solubility of skew left braces and study the ideal structure of soluble skew left braces. As a consequence, results on decomposability of solutions are also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-26T11:59:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T25",
      "16N40",
      "81R50"
    ],
    "keywords": [
      "solubility",
      "finite skew left braces admitting",
      "yang-baxter equation calls",
      "non-degenerate set-theoretic solutions",
      "soluble skew left braces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}