2019/09/06 by Moon, Han-Bom, Wong, Helen · 1 citation
#32G15 #57M20 #57M25 #57M27 #57M50 #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1909.03085
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.