The quantum 2-sphere as a complex quantum manifold

Details The quantum 2-sphere as a complex quantum manifold The quantum 2-sphere as a complex quantum manifold

1995-04-06

arxiv.org/abs/q-alg/9504003v1

Mathematics

Quantum Algebra

19 pages

Scientific paper

We describe the quantum sphere of Podle\'{s} 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.

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