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 $U_q(2)$, $SU_q(2)$, and $SO_q(3) (q \in (-1,0)\cup (0,1])$ arise in this manner and list the idempotent states on compact quantum semigroups $U_o(2)$, $SU_o(2)$, and $SO_o(3)$. In the Appendix we provide a simple proof of coamenability of the deformations of classical compact Lie groups.