CLASSIFICATION OF 3-DIMENSIONAL COVARIANT DIFFERENTIAL CALCULI ON PODLES QUANTUM SPHERES AND ON RELATED SPACES

Covariant differential calculi on the quantum space H(qlambdarho) for the quantum group SL(q)(2) are classified. Our main assumptions are that q is not a root of unity and that the differentials de(j) of the generators of H(qlambdarho) form a free right module basis for the first-order forms. Our result says, in particular, that apart from the two cases c = c(3), infinity there exists a unique differential calculus with the above properties on the space H(qlambdarho) which corresponds to Podles' quantum sphere S(qc)2.