Classification of Idempotent States on the compact quantum groups U_q(2), SU_q(2), and SO_q(3)
Résumé
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 (-1,1] \ {0}) arise in this manner and list the idempotent states on compact quantum semigroups U_0(2), SU_0(2), and SO_0(3). In the Appendix we provide a simple proof of coamenability of the deformations of classical compact Lie groups.