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.

中文翻译：

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罗杰-杨绞球代数和装饰的Teichmüller空间

基于双曲线几何考虑，Roger和Yang引入了包括弧线在内的Kauffman括号绞线代数的扩展。特别地，它们的绞线代数是某个可交换曲线代数的变形量化，并且在装饰的Teichmüller空间上，曲线代数与光滑函数的代数之间存在Poisson代数同构。在本文中，我们考虑的是带有穿孔的表面，该表面不是三孔球面，并且具有理想的三角剖分且没有自折叠边缘或三角形。对于这些曲面，我们证明Roger和Yang的Poisson代数同态是可射性的，并且Skein代数没有零除数。关于法线弧的广义角坐标的部分可能是独立引起关注的。