{
  "id": "2102.00888",
  "version": "v1",
  "published": "2021-02-01T15:01:09.000Z",
  "updated": "2021-02-01T15:01:09.000Z",
  "title": "On values of $\\mathfrak{sl}_3$ weight system on chord diagrams whose intersection graph is complete bipartite",
  "authors": [
    "Zhuoke Yang"
  ],
  "categories": [
    "math.CO",
    "math.GT"
  ],
  "abstract": "Each knot invariant can be extended to singular knots according to the skein rule. A Vassiliev invariant of order at most $n$ is defined as a knot invariant that vanishes identically on knots with more than $n$ double points. A chord diagram encodes the order of double points along a singular knot. A Vassiliev invariant of order $n$ gives rise to a function on chord diagrams with $n$ chords. Such a function should satisfy some conditions in order to come from a Vassiliev invariant. A weight system is a function on chord diagrams that satisfies so-called 4-term relations. Given a Lie algebra $\\mathfrak{g}$ equipped with a non-degenerate invariant bilinear form, one can construct a weight system with values in the center of the universal enveloping algebra $U(\\mathfrak{g})$. In this paper, we calculate $\\mathfrak{sl}_3$ weight system for chord diagram whose intersection graph is complete bipartite graph $K_{2,n}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-01T15:01:09.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chord diagram",
      "weight system",
      "complete bipartite",
      "intersection graph",
      "vassiliev invariant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}