Classification of idempotent states on the compact quantum groups Uq(2), SUq(2), and SOq(3)

Abstract

We give a simple characterisation of those idempotent states on compact quantum groups which arise as Haar states on quantum subgroups, show that all idempotent states on quantum groups Uq(2), SUq(2), and SOq(3) (q 2 (−1, 0) [ (0, 1]) arise in this manner and list the idempotent states on compact quantum semigroups U0(2), SU0(2), and SO0(3). In the Appendix we provide a simple proof of coamenability of the deformations of classical compact Lie groups.