A New Characterisation of Idempotent States on Finite and Compact Quantum Groups

摘要

We show that idempotent states on finite quantum groups correspond topre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows thatthe lattices formed by the idempotent states on a finite quantum group and byits coidalgebras are isomorphic. We show furthermore that these lattices arealso isomorphic for compact quantum groups, if one restricts to expectedcoidalgebras.