  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.
