Work

Quantum direct products and the Künneth class

Year: 2024

Type: article

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 * -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.

Source: Annales mathématiques Blaise Pascal

DOI: 10.5802/ambp.424

Author: Rubén Martos

Institutions: University of Copenhagen, Centre National de la Recherche Scientifique, Université Clermont Auvergne, Laboratoire de Mathématiques Blaise Pascal

Language: English

Topic: Advanced Operator Algebra Research

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

Awards: G434337789, Connes' Conjectures with Quantum Groups