On idempotent states on quantum groups

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

References in corpus (3)

• Compact and discrete subgroups of algebraic quantum groups I
• The Fourier transform in quantum group theory
• On ergodic properties of convolution operators associated with compact quantum groups

Cited by in corpus (13)

• Embeddable Quantum Homogeneous Spaces
• A New Characterisation of Idempotent States on Finite and Compact Quantum Groups
• Quantum flag manifolds, quantum symmetric spaces and their associated universal K-matrices
• Partial actions of C*-quantum groups I: Restriction and Globalization
• Modelling questions for quantum permutations
• The Ergodic Theorem for Random Walks on Finite Quantum Groups
• A state-space approach to quantum permutations
• Berezin Quantization From Ergodic Actions of Compact Quantum Groups, and Quantum Gromov-Hausdorff Distance
• On Square Roots of the Haar State on Compact Quantum Groups
• Invariant integrals on coideals and their Drinfeld doubles
• Modelling questions for transitive quantum groups
• Idempotent states on Sekine quantum groups
• Diaconis-Shahshahani Upper Bound Lemma for Finite Quantum Groups