{
  "id": "0909.2545",
  "version": "v2",
  "published": "2009-09-14T13:33:35.000Z",
  "updated": "2010-07-15T10:53:03.000Z",
  "title": "An adelic extension of the Jones polynomial",
  "authors": [
    "Jesus Juyumaya",
    "Sofia Lambropoulou"
  ],
  "comment": "15 pages, 1 figure",
  "journal": "1. M. Banagl, D. Vogel (eds.) The mathematics of knots, Contributions in the Mathematical and Computational Sciences, Vol. 1, Springer 2010",
  "categories": [
    "math.GT",
    "math.QA"
  ],
  "abstract": "In this paper we represent the classical braids in the Yokonuma--Hecke and the adelic Yokonuma--Hecke algebras. More precisely, we define the completion of the framed braid group and we introduce the adelic Yokonuma--Hecke algebras, in analogy to the $p$--adic framed braids and the $p$--adic Yokonuma--Hecke algebras introduced in \\cite{jula,jula2}. We further construct an adelic Markov trace, analogous to the $p$--adic Markov trace constructed in \\cite{jula2}, and using the traces in \\cite{ju} and the adelic Markov trace we define topological invariants of classical knots and links, upon imposing some condition. Each invariant satisfies a cubic skein relation coming from the Yokonuma--Hecke algebra.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-07-15T10:53:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57M27",
      "20F38",
      "20F36",
      "20C08"
    ],
    "keywords": [
      "jones polynomial",
      "adelic extension",
      "adelic markov trace",
      "adelic yokonuma-hecke algebras",
      "adic markov trace"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2545J"
    }
  }
}