Instantons on the quantum 4-spheres S4q

We introduce noncommutative algebras A(q) of quantum 4-spheres S-q(4), with q is an element of R, defined via a suspension of the quantum group SUq (2), and a quantum instanton bundle described by a selfadjoint idempotent e is an element of Mat(4)(A(q)), e(2) = e = e*. Contrary to what happens for the classical case or for the noncommutative instanton constructed in [8], the first Chern-Connes class ch(1) (e) does not vanish thus signaling a dimension drop. The second Chern-Connes class ch(2)(e) does not vanish as well and the couple (ch(1) (e), ch(2)(e)) defines a cycle in the (b, B) bicomplex of cyclic homology.