{
  "id": "2202.10754",
  "version": "v1",
  "published": "2022-02-22T09:15:30.000Z",
  "updated": "2022-02-22T09:15:30.000Z",
  "title": "A homogeneous presentation of symmetric quandles",
  "authors": [
    "Yuta Taniguchi"
  ],
  "comment": "6 pages",
  "categories": [
    "math.GT"
  ],
  "abstract": "A quandle is an algebraic structure whose axioms correspond to the Reidemeister moves of knot theory. S. Kamada introduced the notion of a quandle with a good involution, which is later called a symmetric quandle. We are interested in the algebraic structure of symmetric quandles. Given a group $G$, an element $z$ and a certain subgroup $H$, one can obtain the quandle. D. Joyce showed that every quandle is isomorphic to the disjoint union of such quandles. In this paper, given a group $G$, elements $z,r$ in $G$ and a certain subgroup $H$, we construct a symmetric quandle. Futhermore, we show that every symmetric quandle is isomorphic to the disjoint union of such quandles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-22T09:15:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57K10",
      "57K12"
    ],
    "keywords": [
      "symmetric quandle",
      "homogeneous presentation",
      "algebraic structure",
      "disjoint union",
      "knot theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}