IDEMPOTENT STATES ON QUANTUM GROUPS VIA VON NEUMANN ALGEBRAS

We study idempotent states on locally compact quantum groups and its dual quantum groups and figure out their relations with quantum subgroups. We establish a one to one correspondence between idempotent states on a locally compact quantum groups G and integrable coideal von Neumann subalgebras of L1(G) that are preserved by the scaling group. We also establish a one to one correspondence between open quantum subgroups of G and central idempotent states on the dual quantum groupbG.

Keywords:

Coideals , idempotent states , locally compact quantum groups , quantum subgroups.