Idempotent states on compact quantum groups and their classification on U_q(2), SU_q(2), and SO_q(3)

Details Idempotent states on compact quantum groups and their classification on U_q(2), SU_q(2), and SO_q(3) Idempotent states on compact quantum groups and their classification on U_q(2), SU_q(2), and SO_q(3)

2009-03-13

arxiv.org/abs/0903.2363v2

Mathematics

Operator Algebras

32 pages; version 2 revises the terminology, adds a few new results in Section 3 and introduces several minor corrections. The

Scientific paper

Unlike for locally compact groups, idempotent states on locally compact quantum groups do not necessarily arise as Haar states of compact quantum subgroups. We give a simple characterisation of those idempotent states on compact quantum groups which do arise as Haar states on quantum subgroups. We also show that all idempotent states on the 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 the compact quantum semigroups U_0(2), SU_0(2), and SO_0(3). In the Appendix we provide a short new proof of coamenability of the deformations of classical compact Lie groups based on their representation theory.

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