1995/04/06 by Chong-Sun Chu, Chu, Chong-Sun, Pei-Ming Ho +3
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #q-alg
paper · pdf · doi:10.48550/arxiv.q-alg/9504003
19 pages
arxiv created 1995/04/06 · arxiv updated 2009/11/30
We describe the quantum sphere of Podleś for c=0 by means of a stereographic projection which is analogous to that which exhibits the classical sphere as a complex manifold. We show that the algebra of functions and the differential calculus on the sphere are covariant under the coaction of fractional transformations with \SU coefficients as well as under the action of \SU vector fields. Going to the classical limit we obtain the Poisson sphere. Finally, we study the invariant integration of functions on the sphere and find its relation with the translationally invariant integration on the complex quantum plane.