{
  "id": "1810.03027",
  "version": "v1",
  "published": "2018-10-06T17:14:57.000Z",
  "updated": "2018-10-06T17:14:57.000Z",
  "title": "Constructing biquandles",
  "authors": [
    "Eva Horvat"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR",
    "math.GT"
  ],
  "abstract": "We define biquandle structures on a given quandle, and show that any biquandle is given by some biquandle structure on its underlying quandle. We characterize all biquandles with a given underlying quandle. Using this characterization, we obtain a relationship between the automorphism group of a biquandle and the automorphism group of its underlying quandle. As an application, we determine the automorphism groups of Alexander and dihedral biquandles. We also define a biquandle structure on a direct product of two quandles and describe the automorphism group of the biquandle thus obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-06T17:14:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphism group",
      "constructing biquandles",
      "define biquandle structures",
      "direct product",
      "dihedral biquandles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}