{
  "id": "1606.06151",
  "version": "v1",
  "published": "2016-06-20T14:50:28.000Z",
  "updated": "2016-06-20T14:50:28.000Z",
  "title": "Classification of 8-dimensional rank two commutative semifields",
  "authors": [
    "Michel Lavrauw",
    "Morgan Rodgers"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "We classify the rank two commutative semifields which are 8-dimensional over their center $\\mathbb{F}_{q}$. This is done using computational methods utilizing the connection to linear sets in $\\mathrm{PG}(2,q^{4})$. We then apply our methods to complete the classification of rank two commutative semifields which are 10-dimensional over $\\mathbb{F}_{3}$. The implications of these results are detailed for other geometric structures such as semifield flocks, ovoids of parabolic quadrics, and eggs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-20T14:50:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "51E20",
      "12K10"
    ],
    "keywords": [
      "commutative semifields",
      "classification",
      "parabolic quadrics",
      "geometric structures",
      "semifield flocks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}