A Hopf bundle over a quantum four-sphere from the symplectic group

We construct a quantum version of the SU(2) Hopf bundle S-7 -> S-4. The quantum sphere S-q(7) arises from the symplectic group Sp(q)(2) and a quantum 4-sphere S-q(4) is obtained via a suitable self-adjoint idempotent p whose entries generate the algebra A(S-q(4)) of polynomial functions over it. This projection determines a deformation of an (anti-)instanton bundle over the classical sphere S-4. We compute the fundamental K-homology class of S-q(4) and pair it with the class of p in the K-theory getting the value -1 for the topological charge. There is a right coaction of SUq(2) on S-q(7) such that the algebra A(S-q(7)) is a non-trivial quantum principal bundle over A(S-q(7)) with structure quantum group A(SUq(2)).