English

On idempotent states on quantum groups

Quantum Algebra 2009-09-04 v3 Probability

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.

Keywords

Cite

@article{arxiv.0808.1683,
  title  = {On idempotent states on quantum groups},
  author = {Uwe Franz and Adam Skalski},
  journal= {arXiv preprint arXiv:0808.1683},
  year   = {2009}
}

Comments

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

R2 v1 2026-06-21T11:09:42.489Z