Equivariant Comparison of Quantum Homogeneous Spaces

We consider the quantum homogeneous spaces of the q-deformation of simply connected simple compact Lie groups and their Poisson–Lie quantum subgroups. We prove the deformation invariance in the equivariant KK-theory with respect to the translation action by maximal tori. This extends a result of Neshveyev and Tuset to the equivariant setting. As applications, we prove the ring isomorphism of the K-homology of G _q with respect to the coproduct of C(G _q ), and an analogue of the Borsuk–Ulam theorem for quantum spheres.