Quantum group-twisted tensor products of C*-algebras II

TL;DR

This paper develops a monoidal structure for coactions of quasitriangular C*-quantum groups, introduces braided C*-quantum groups, and shows how they relate to compact quantum groups via semidirect products.

Contribution

It extends twisted tensor products to a monoidal framework and defines braided C*-quantum groups with new structural properties.

Findings

Established a monoidal structure on coactions of quasitriangular C*-quantum groups

Defined braided C*-quantum groups with twisted comultiplication

Demonstrated that compact braided C*-quantum groups form compact quantum groups via semidirect products

Abstract

For a quasitriangular C*-quantum group, we enrich the twisted tensor product constructed in the first part of this series to a monoidal structure on the category of its continuous coactions on C*-algebras. We define braided C*-quantum groups, where the comultiplication takes values in a twisted tensor product. We show that compact braided C*-quantum groups yield compact quantum groups by a semidirect product construction.