00942nas a2200109   4500008004300000245005300043210005300096520060100149100002000750700002600770856003600796       2005                        en_Ud  00aPrincipal fibrations from noncommutative spheres0 aPrincipal fibrations from noncommutative spheres3 aWe construct noncommutative principal fibrations S_\\\\theta^7 \\\\to S_\\\\theta^4 which are deformations of the classical SU(2) Hopf fibration over the four sphere. We realize the noncommutative vector bundles associated to the irreducible representations of SU(2) as modules of coequivariant maps and construct corresponding projections. The index of Dirac operators with coefficients in the associated bundles is computed with the Connes-Moscovici local index formula. The algebra inclusion $A(S_\\\\theta^4) \\\\into A(S_\\\\theta^7)$ is an example of a not trivial quantum principal bundle.1 aLandi, Giovanni1 avan Suijlekom, Walter  uhttp://hdl.handle.net/1963/2284