{
  "id": "0708.1685",
  "version": "v2",
  "published": "2007-08-13T10:16:24.000Z",
  "updated": "2009-07-11T14:27:14.000Z",
  "title": "Vector bundles on degenerations of elliptic curves and Yang-Baxter equations",
  "authors": [
    "Igor Burban",
    "Bernd Kreussler"
  ],
  "comment": "140 pages, extended version, some typos corrected",
  "categories": [
    "math.AG",
    "math.QA"
  ],
  "abstract": "In this paper we introduce the notion of a geometric associative r-matrix attached to a genus one fibration with a section and irreducible fibres. It allows us to study degenerations of solutions of the classical Yang-Baxter equation using the approach of Polishchuk. We also calculate certain solutions of the classical, quantum and associative Yang-Baxter equations obtained from moduli spaces of (semi-)stable vector bundles on Weierstrass cubic curves.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-07-11T14:27:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "14H60",
      "14D06",
      "14H70"
    ],
    "keywords": [
      "elliptic curves",
      "weierstrass cubic curves",
      "geometric associative r-matrix",
      "moduli spaces",
      "associative yang-baxter equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 140,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1685B"
    }
  }
}