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Pré-Publication, Document De Travail Année : 2024

Quantum direct products and the Künneth class

Résumé

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*-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.
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Dates et versions

hal-04442334 , version 1 (06-02-2024)

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Rubén Martos. Quantum direct products and the Künneth class. 2024. ⟨hal-04442334⟩

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