Fatemeh Khosravi
Paweª Kasprzak

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.

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