The Braided Quantum 2-Sphere

Abstract

In a recent paper the quantum 2-sphere $S^2_q$ was described as a quantum complex manifold. Here we consider several copies of $S^2_q$ and derive their braiding commutation relations. The braiding is extended to the differential and to the integral calculus on the spheres. A quantum analogue of the classical anharmonic ratio of four points on the sphere is given, which is invariant under the coaction of $SU_q(2)$.