Quantum direct products and the Künneth class

Abstract

We introduce a Künneth class in the quantum equivariant setting inspired by the pioneer work by J. Chabert, H. Oyono-Oyono and S. Echterhoff, which allows to relate the quantum Baum-Connes property with the Künneth formula by generalising some key results of Chabert-Oyono-Oyono-Echterhoff to discrete quantum groups. Finally, we make the observation that the C${}^{\ast }$-algebra defining a compact quantum group with dual satisfying the strong quantum Baum-Connes property belongs to the Künneth class. This allows to obtain some K-theory computations for quantum direct products based on earlier work by Voigt and Vergnioux-Voigt.

Accepted for publication in Annales Mathematiques Blaise Pascal

References in corpus (2)

• Free wreath product quantum groups : the monoidal category, approximation properties and free probability
• Permanence of the torsion-freeness property for divisible discrete quantum subgroups