A new characterisation of idempotent states on finite and compact quantum groups
Copyright policy )A new characterisation of idempotent states on finite and compact quantum groups
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.
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], States of selfadjoint operator algebras, 46L65, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics - Operator Algebras, Quantizations, deformations for selfadjoint operator algebras, 17B37, 620, 510, Mathematics - Quantum Algebra, 17B37; 43A05; 46L65, [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], FOS: Mathematics, Quantum Algebra (math.QA), [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), 43A05, Ring-theoretic aspects of quantum groups
[MATH.MATH-QA] Mathematics [math]/Quantum Algebra [math.QA], States of selfadjoint operator algebras, 46L65, [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA], Mathematics - Operator Algebras, Quantizations, deformations for selfadjoint operator algebras, 17B37, 620, 510, Mathematics - Quantum Algebra, 17B37; 43A05; 46L65, [MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA], FOS: Mathematics, Quantum Algebra (math.QA), [MATH.MATH-OA] Mathematics [math]/Operator Algebras [math.OA], Operator Algebras (math.OA), 43A05, Ring-theoretic aspects of quantum groups
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