Equivariant comparison of quantum homogeneous spaces

TL;DR

This paper proves the deformation invariance of quantum homogeneous spaces in equivariant KK-theory, extending previous results and applying them to K-theory ring isomorphisms and quantum sphere analogues.

Contribution

It extends deformation invariance results to the equivariant setting and applies them to quantum K-theory and Borsuk-Ulam type theorems for quantum spheres.

Findings

K-group of Gq is ring isomorphic to the coproduct of C(Gq)

Deformation invariance holds in equivariant KK-theory

Quantum spheres satisfy an analogue of the Borsuk-Ulam theorem

Abstract

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