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

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Franz, Uwe
Skalski, Adam
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Abstract
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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.
Comment: 9 pages
Keywords
Mathematics - Operator Algebras, Mathematics - Quantum Algebra, 17B37, 43A05, 46L65
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