{
  "id": "2102.06104",
  "version": "v1",
  "published": "2021-02-11T16:37:18.000Z",
  "updated": "2021-02-11T16:37:18.000Z",
  "title": "Abelian maps, brace blocks, and solutions to the {Y}ang-{B}axter equation",
  "authors": [
    "Alan Koch"
  ],
  "comment": "15 pages",
  "categories": [
    "math.GR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Let $G$ be a finite nonabelian group. We show how an endomorphism of $G$ with abelian image gives rise to a family of binary operations $\\{\\circ_n: n\\in \\mathbb Z^{\\ge 0}\\}$ on $G$ such that $(G,\\circ_m,\\circ_n)$ is a skew left brace for all $m,n\\ge 0$. A brace block gives rise to a number of non-degenerate set-theoretic solutions to the Yang-Baxter equation. We give examples showing that the number of solutions obtained can be arbitrarily large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-11T16:37:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16T25",
      "20N99"
    ],
    "keywords": [
      "brace block",
      "abelian maps",
      "non-degenerate set-theoretic solutions",
      "finite nonabelian group",
      "skew left brace"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}