The Roger-Yang skein algebra and the decorated Teichmuller space

Han-Bom Moon, Helen Wong

Published 2019-09-06Version 1

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.