Quantum direct products and the K\"unneth class
Operator Algebras
2024-12-30 v3 Category Theory
K-Theory and Homology
Quantum Algebra
Abstract
We introduce a K\"unneth 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 K\"unneth 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 K\"unneth class. This allows to obtain some K-theory computations for quantum direct products based on earlier work by Voigt and Vergnioux-Voigt.
Cite
@article{arxiv.2303.09217,
title = {Quantum direct products and the K\"unneth class},
author = {Rubén Martos},
journal= {arXiv preprint arXiv:2303.09217},
year = {2024}
}
Comments
Accepted for publication in Annales Mathematiques Blaise Pascal