The Roger–Yang skein algebra and the decorated Teichmüller space

  • Han-Bom Moon

    Fordham University, New York, USA
  • Helen Wong

    Claremont McKenna College, USA
The Roger–Yang skein algebra and the decorated Teichmüller space cover
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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 Teichmüller space. In this paper, we consider surfaces with punctures which are 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 has no zero divisors. A section about generalized corner coordinates for normal arcs may be of independent interest.

Cite this article

Han-Bom Moon, Helen Wong, The Roger–Yang skein algebra and the decorated Teichmüller space. Quantum Topol. 12 (2021), no. 2, pp. 265–308

DOI 10.4171/QT/150