On idempotent states on quantum groups

Details On idempotent states on quantum groups On idempotent states on quantum groups

2008-08-12

arxiv.org/abs/0808.1683v3

Journal of Algebra, Vol. 322, no. 5, pp. 1774-1802, 2009

Mathematics

Quantum Algebra

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 appe

Scientific paper

10.1016/j.jalgebra.2009.05.037

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.

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