The aim of this talk is to show the equivalence of three closely related 'freeness' conditions for a compact quantum group action on a unital C*-algebra: saturatedness (in the sense of Rieffel), the Ellwood density condition, and the underlying Hopf algebra coaction being Galois. This provides in particular a purely algebraic framework in which to treat compact quantum principal bundles.

This talk is based on joint work with M. Yamashita, and with P.F. Baum and P.M. Hajac.