{
  "id": "1602.07203",
  "version": "v1",
  "published": "2016-02-23T15:40:56.000Z",
  "updated": "2016-02-23T15:40:56.000Z",
  "title": "Classical link invariants from the framizations of the Iwahori-Hecke algebra and of the Temperley-Lieb algebra of type $A$",
  "authors": [
    "Dimos Goundaroulis",
    "Sofia Lambropoulou"
  ],
  "comment": "26 pages, 6 figures",
  "categories": [
    "math.GT"
  ],
  "abstract": "In this paper we first present the construction of the new 2-variable classical link invariants arising from the Yokonuma-Hecke algebras ${\\rm Y}_{d,n}(q)$, which are not topologically equivalent to the Homflypt polynomial. We then present the algebra ${\\rm FTL}_{d,n}(q)$ which is the appropriate Temperley-Lieb analogue of ${\\rm Y}_{d,n}(q)$, as well as the related 1-variable classical link invariants, which in turn are not topologically equivalent to the Jones polynomial. Finally, we present the algebra of braids and ties which is related to the Yokonuma-Hecke algebra, and also its quotient, the partition Temperley-Lieb algebra ${\\rm PTL}_n(q)$ and we prove an isomorphism of this algebra with a subalgebra of ${\\rm FTL}_{d,n}(q)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-23T15:40:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M25",
      "20C08",
      "20F36",
      "57M27"
    ],
    "keywords": [
      "classical link invariants",
      "iwahori-hecke algebra",
      "framizations",
      "yokonuma-hecke algebra",
      "topologically equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160207203G"
    }
  }
}