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

Abstract: We compare actions on C*-algebras of two constructions of locally compact quantum groups, the bicrossed product due to Vaes-Vainerman and the double crossed product due to Baaj-Vaes. We give a one-to-one correspondence between them up to Morita equivalence, in the same spirit as Takesaki-Takai and Baaj-Skandalis dualities. This includes a duality between a quantum double and the product of the original quantum group with its opposite. We will explain its consequences for equivariant Kasparov theory in relation to the quantum analog of the Baum-Connes conjecture.

operator algebrasquantum algebra

Audience: researchers in the topic

Quantum Groups Seminar [QGS]

Series comments: This seminar aims to bring together experts in the area of quantum groups. The seminar topics will cover the theory of quantum groups and related structures in a large sense: Hopf algebras, operator algebras, q-deformations, higher categories and related branches of noncommutative mathematics.

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