A New Characterisation of Idempotent States on Finite and Compact Quantum Groups
arXiv:0906.2362 · doi:10.1016/j.crma.2009.06.015
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.
9 pages