{
  "id": "2106.11727",
  "version": "v1",
  "published": "2021-06-22T13:01:36.000Z",
  "updated": "2021-06-22T13:01:36.000Z",
  "title": "Gyrogroup through its Grothendieck Group Completion and Right gyrogroup action",
  "authors": [
    "Akshay Kumar",
    "Mani Shankar Pandey",
    "Seema Kushwaha",
    "Sumit Kumar Upadhyay"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "In this article, we discuss the Grothendieck group completion (GGC) of a gyrogroup. Consequently, we show that there is a one to one correspondence between actions and representations of a gyrogroup, and actions and representations of its Grothendieck group completion. We also introduce the concept of an action of a right gyrogroup.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-22T13:01:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "grothendieck group completion",
      "right gyrogroup action",
      "representations",
      "correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}