{
  "id": "2203.12174",
  "version": "v1",
  "published": "2022-03-23T03:32:08.000Z",
  "updated": "2022-03-23T03:32:08.000Z",
  "title": "Post-Hopf algebras, relative Rota-Baxter operators and solutions of the Yang-Baxter equation",
  "authors": [
    "Yunnan Li",
    "Yunhe Sheng",
    "Rong Tang"
  ],
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, first we introduce the notion of a post-Hopf algebra, which gives rise to a post-Lie algebra on the space of primitive elements and there is naturally a post-Hopf algebra structure on the universal enveloping algebra of a post-Lie algebra. A novel property is that a cocommutative post-Hopf algebra gives rise to a generalized Grossman-Larsson product, which leads to a subadjacent Hopf algebra and can be used to construct solutions of the Yang-Baxter equation. Then we introduce the notion of relative Rota-Baxter operators on Hopf algebras. A cocommutative post-Hopf algebra gives rise to a relative Rota-Baxter operator on its subadjacent Hopf algebra. Conversely, a relative Rota-Baxter operator also induces a post-Hopf algebra. Then we show that relative Rota-Baxter operators give rise to matched pairs of Hopf algebras. Consequently, post-Hopf algebras and relative Rota-Baxter operators give solutions of the Yang-Baxter equation in certain cocommutative Hopf algebras. Finally we characterize relative Rota-Baxter operators on Hopf algebras using relative Rota-Baxter operators on the Lie algebra of primitive elements, graphs and module bialgebra structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-23T03:32:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "relative rota-baxter operator",
      "yang-baxter equation",
      "subadjacent hopf algebra",
      "cocommutative post-hopf algebra",
      "post-lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}