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

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

2009-06-12

arxiv.org/abs/0906.2362v1

Comptes Rendus Mathematique Vol. 347, pp. 991-996, 2009

Mathematics

Operator Algebras

9 pages

Scientific paper

10.1016/j.crma.2009.06.015

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.

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