Partial Pontryagin duality for actions of quantum groups on C*-algebras
Operator Algebras
2023-09-19 v3 K-Theory and Homology
Quantum Algebra
Abstract
We compare actions on C*-algebras of two constructions of locally compact quantum groups, the bicrossed product and the double crossed product. We give a duality between them as a generalization of Baaj-Skandalis duality. In the case of quantum doubles, this duality also preserves monoidal structures given by twisted tensor products. We also discuss its consequences for equivariant Kasparov theories in relation to the quantum analogue of the Baum-Connes conjecture.
Keywords
Cite
@article{arxiv.2210.12838,
title = {Partial Pontryagin duality for actions of quantum groups on C*-algebras},
author = {Kan Kitamura},
journal= {arXiv preprint arXiv:2210.12838},
year = {2023}
}
Comments
29 pages, added Remark 6.13 and improved exposition