{
  "id": "2312.01337",
  "version": "v1",
  "published": "2023-12-03T09:55:44.000Z",
  "updated": "2023-12-03T09:55:44.000Z",
  "title": "Relative Rota-Baxter operators of weight 0 on groups, pre-groups, braces, the Yang-Baxter equation and $T$-structures",
  "authors": [
    "Yunnan Li",
    "Yunhe Sheng",
    "Rong Tang"
  ],
  "comment": "21 pages",
  "categories": [
    "math-ph",
    "math.GR",
    "math.MP",
    "math.RA"
  ],
  "abstract": "In this paper, we study relative Rota-Baxter operators of weight $0$ on groups and give various examples. In particular, we propose different approaches to study Rota-Baxter operators of weight $0$ on groups and Lie groups. We establish various explicit relations among relative Rota-Baxter operators of weight $0$ on groups, pre-groups, braces, set-theoretic solutions of the Yang-Baxter equation and $T$-structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-03T09:55:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "yang-baxter equation",
      "structures",
      "pre-groups",
      "study relative rota-baxter operators",
      "study rota-baxter operators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}