{
  "id": "1410.5207",
  "version": "v1",
  "published": "2014-10-20T09:49:17.000Z",
  "updated": "2014-10-20T09:49:17.000Z",
  "title": "Construction of an AS-regular sub-$\\mathbb{Z}$-algebra of the 2-veronese of an AS-regular algebra",
  "authors": [
    "Michel Van den Bergh",
    "Dennis Presotto"
  ],
  "comment": "19 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper we generalize some classical birational transformations to the non-commutative case. In particular we show that 3-dimensional quadratic Sklyanin algebras (non-commutative projective planes) and 3-dimensional cubic Sklyanin algebras (non-commutative quadrics) have the same function field. In the same vein we construct and analogue of the Cremona transform for non-commutative projective planes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-20T09:49:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A22"
    ],
    "keywords": [
      "as-regular algebra",
      "construction",
      "non-commutative projective planes",
      "quadratic sklyanin algebras",
      "cubic sklyanin algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5207V"
    }
  }
}