{
  "id": "1503.07894",
  "version": "v1",
  "published": "2015-03-13T14:00:34.000Z",
  "updated": "2015-03-13T14:00:34.000Z",
  "title": "Classification of subspaces in ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3$ and orbits in ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3\\otimes {\\mathbb{F}}^r$",
  "authors": [
    "Michel Lavrauw",
    "John Sheekey"
  ],
  "categories": [
    "math.CO",
    "math.AG"
  ],
  "abstract": "This paper contains the classification of the orbits of elements of the tensor product spaces ${\\mathbb{F}}^2\\otimes {\\mathbb{F}}^3 \\otimes{\\mathbb{F}}^r$, $r\\geq 1$, under the action of two natural groups, for all finite; real; and algebraically closed fields. For each of the orbits we determine: a canonical form; the tensor rank; the rank distribution of the contraction spaces; and a geometric description. The proof is based on the study of the contraction spaces in ${\\mathrm{PG}}({\\mathbb{F}}^2\\otimes{\\mathbb{F}}^3)$ and is geometric in nature. Although the main focus is on finite fields, the techniques are mostly field independent.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-13T14:00:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classification",
      "contraction spaces",
      "tensor product spaces",
      "paper contains",
      "natural groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150307894L"
    }
  }
}