The automatic imprimitivity for Gq

Abstract

Let Gq be the Drinfeld-Jimbo deformation of a connected simply-connected compact Lie group and T be its maximal torus. We show that the induction functors from the categories of T-equivariant correspondences to the categories of Gq-equivariant correspondences give equivalences of these categories under the existence of tracial states. As its application, we show some automatic imprimitivity results and classification results for extensions, subalgebras and finite index discrete quantum subgroups of Gqˆ.