{
  "id": "2105.00428",
  "version": "v1",
  "published": "2021-05-02T09:15:34.000Z",
  "updated": "2021-05-02T09:15:34.000Z",
  "title": "Rota-Baxter groups, skew left braces, and the Yang-Baxter equation",
  "authors": [
    "Valeriy G. Bardakov",
    "Vsevolod Gubarev"
  ],
  "comment": "24 p",
  "categories": [
    "math.GR",
    "math.QA"
  ],
  "abstract": "Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang-Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. Recently, L. Guo, H. Lang, Y. Sheng [arXiv:2009.03492] gave a definition of what is a Rota-Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota-Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota-Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota-Baxter group. We interpret theory of skew left braces in terms of Rota -- Baxter operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-02T09:15:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T25",
      "20N99"
    ],
    "keywords": [
      "skew left brace",
      "rota-baxter group",
      "quantum yang-baxter equation",
      "baxter operators",
      "general notion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}