{
  "id": "1912.03091",
  "version": "v1",
  "published": "2019-12-06T12:51:49.000Z",
  "updated": "2019-12-06T12:51:49.000Z",
  "title": "From Braces to Hecke algebras & Quantum Groups",
  "authors": [
    "Anastasia Doikou",
    "Agata Smoktunowicz"
  ],
  "comment": "26 pages, LaTex",
  "categories": [
    "math-ph",
    "math.MP",
    "math.RA"
  ],
  "abstract": "We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras and we identify new quantum groups associated to set-theoretic solutions coming from braces. We also construct a novel class of quantum discrete integrable systems and we derive symmetries for the corresponding periodic transfer matrices.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-06T12:51:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum groups",
      "hecke algebras",
      "corresponding periodic transfer matrices",
      "quantum discrete integrable systems",
      "quantum integrable systems"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}