Journal of Operator Theory

Volume 93, Issue 1, Winter 2025 pp. 173-216.

Partial Pontryagin duality for actions of quantum groups on $C^*$ -algebras

Authors: Kan Kitamura
Author institution: Graduate School of Mathematical Sciences, the University of Tokyo, 3-8-1 Komaba Meguro-ku Tokyo 153-8914, Japa

Summary: We compare actions on $C^*$ -algebras of two constructions of locally compact quantum groups, the bicrossed product and the double crossed product. We give a duality between them as a generalization of Baaj--Skandalis duality. In the case of quantum doubles, this duality also preserves monoidal structures given by twisted tensor products. We also discuss its consequences for equivariant Kasparov theories in relation to the quantum analogue of the Baum--Connes conjecture.

DOI: http://dx.doi.org/10.7900/jot.2023ian21.241
Keywords: locally compact quantum group, quantum double, Takesaki-Takai duality, Baum-Connes conjecture

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