On idempotent states on quantum groups
arXiv:0808.1683 · doi:10.1016/j.jalgebra.2009.05.037
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.
28 pages; v3 omits the former lemma 2.1 due to a gap in the proof. This does not affect any other results. The paper will appear in the Journal of Algebra