, Volume 317, Issue 3, pp 593-614

Equivariant Comparison of Quantum Homogeneous Spaces

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Abstract

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.

Communicated by Y. Kawahigashi
Supported in part by the ERC Advanced Grant 227458 OACFT “Operator Alge bras and Conformal Field Theory”.