{
  "id": "1909.03085",
  "version": "v1",
  "published": "2019-09-06T18:21:16.000Z",
  "updated": "2019-09-06T18:21:16.000Z",
  "title": "The Roger-Yang skein algebra and the decorated Teichmuller space",
  "authors": [
    "Han-Bom Moon",
    "Helen Wong"
  ],
  "comment": "34 pages, comments are welcome",
  "categories": [
    "math.GT",
    "math.AG",
    "math.QA"
  ],
  "abstract": "Based on hyperbolic geometric considerations, Roger and Yang introduced an extension of the Kauffman bracket skein algebra that includes arcs. In particular, their skein algebra is a deformation quantization of a certain commutative curve algebra, and there is a Poisson algebra homomorphism between the curve algebra and the algebra of smooth functions on decorated Teichmuller space. In this paper, we consider surfaces with punctures which is not the 3-holed sphere and which have an ideal triangulation without self-folded edges or triangles. For those surfaces, we prove that Roger and Yang's Poisson algebra homomorphism is injective, and the skein algebra they defined have no zero divisors. A section about generalized corner coordinates for normal arcs may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-06T18:21:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32G15",
      "57M20",
      "57M25",
      "57M27",
      "57M50"
    ],
    "keywords": [
      "decorated teichmuller space",
      "roger-yang skein algebra",
      "kauffman bracket skein algebra",
      "yangs poisson algebra homomorphism",
      "curve algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}