The quantum 2-sphere as a complex quantum manifold
Journal
Zeitschrift fur Physik C-Particles and Fields
Journal Volume
70
Journal Issue
2
Pages
339-344
Date Issued
1996
Author(s)
Abstract
We describe the quantum sphere of Podleś for c = 0 by means of a stereographic projection which is analogous to that which exibits 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 SUq(2) coefficients as well as under the action of SUq(2) 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. © Springer-Verlag 1996.
Type
journal article