On idempotent states on quantum groups

  title={On idempotent states on quantum groups},
  author={U. Franz and Adam G. Skalski},
  journal={Journal of Algebra},
Abstract Idempotent states on a compact quantum group are shown to yield group-like projections in the multiplier algebra of the dual discrete quantum group. This allows to deduce that every idempotent state on a finite quantum group arises in a canonical way as the Haar state on a finite quantum hypergroup. A natural order structure on the set of idempotent states is also studied and some examples discussed.