A New Characterisation of Idempotent States on Finite and Compact Quantum Groups

Abstract

We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idempotent states on a finite quantum group and by its coidalgebras are isomorphic. We show furthermore that these lattices are also isomorphic for compact quantum groups, if one restricts to expected coidalgebras.

arXiv comment9 pages

References in corpus (5)

• Symmetries of quantum spaces. Subgroups and quotient spaces of quantum $SU(2)$ and $SO(3)$ groups
• Co-Amenability of compact quantum groups
• Notes on Compact Quantum Groups
• On idempotent states on quantum groups
• Compact and discrete subgroups of algebraic quantum groups I

Cited by in corpus (3)

• Embeddable Quantum Homogeneous Spaces
• Integration over the quantum diagonal subgroup and associated Fourier-like algebras
• On Square Roots of the Haar State on Compact Quantum Groups