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Partial Pontryagin duality for actions of quantum groups on C*-algebras (2210.12838v3)
Published 23 Oct 2022 in math.OA, math.KT, and math.QA
Abstract: 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.