2013/09/13 by Leonid Chekhov, Chekhov, Leonid, Marta Mazzocco +1
Mathematics · Physics and Astronomy · #17B37 #57M15 #57Q15 #81R50 #81R60 #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Compact Riemann surface #Conformal map #FOS: Mathematics #FOS: Physical sciences #Geodesic #Geometry #High Energy Physics - Theory (hep-th) #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Mathematical analysis #Mathematical physics #Mathematics #Orbifold #Physics #Pure mathematics #Quantum #Quantum Algebra (math.QA) #Quantum mechanics #Riemann hypothesis #Riemann surface #Surface (topology) #Uniformization (probability theory) #hep-th #math-ph #math.MP #math.QA #msc:17B37 #msc:57M15 #msc:57Q15 #msc:81R50 #msc:81R60
paper · pdf · doi:10.48550/arxiv.1309.3493
published in arXiv (Cornell University) (Cornell University) · 22 pages; 6 figures in LaTeX; contribution to AMS volume dedicated to the 75th birthday of S.P.Novikov
arxiv created 2013/09/13 · openalex publication_date 2013/09/13 · arxiv updated 2013/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
We determine the explicit quantum ordering for a special class of quantum geodesic functions corresponding to geodesics joining exactly two orbifold points or holes on a non-compact Riemann surface. We discuss some special cases in which these quantum geodesic functions form sub--algebras of some abstract algebras defined by the reflection equation and we extend our results to the quantisation of matrix elements of the Fuchsian group associated to the Riemann surface in Poincaré uniformization. In particular we explore an interesting relation between the deformed Uq(\mathfraksl2) and the Zhedanov algebra AW(3).