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Takesaki duality for weights on locally compact quantum group covariant systems. (English) Zbl 1036.46056

Summary: Takesaki duality for weights on a covariant system based on an action of a locally compact quantum group (in the sense of J. Kustermans and S. Vaes) on a von Neumann algebra is shown. In the course of proving the duality, we also introduce a notion of Radon-Nikodym derivative with respect to an action and a weight.

MSC:

46L65 Quantizations, deformations for selfadjoint operator algebras
22D25 \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
46L10 General theory of von Neumann algebras
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
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