Geometry of Quantum Spheres

Spectral triples on the q-deformed spheres of dimension two and three are reviewed.Comment: 23 pages, revie

Quantum spin coverings and statistics

SL_q(2) at odd roots of unity q^l =1 is studied as a quantum cover of the complex rotation group SO(3,C), in terms of the associated Hopf algebras of (quantum) polynomial functions. We work out the irreducible corepresentations, the decomposition of their tensor products and a coquasitriangular structure, with the associated braiding (or statistics). As an example, the case l=3 is discussed in detail.Comment: 15 page