Quantum symmetries of the twisted tensor products of C*-algebras

TL;DR

This paper investigates the quantum symmetry groups of twisted tensor products of C*-algebras with orthogonal filtrations, revealing they are often generalized Drinfeld doubles, with applications to crossed products and specific examples.

Contribution

It computes quantum symmetry groups for twisted tensor products of C*-algebras, extending understanding of their structure and symmetry in noncommutative geometry.

Findings

Quantum symmetry groups are generalized Drinfeld doubles under certain conditions.

Application to crossed products of C*-algebras by discrete group actions.

Counterexample where the main theorem's hypothesis fails, and the symmetry group differs.

Abstract

We consider the construction of twisted tensor products in the category of C*-algebras equipped with orthogonal filtrations and under certain assumptions on the form of the twist compute the corresponding quantum symmetry group, which turns out to be the generalised Drinfeld double of the quantum symmetry groups of the original filtrations. We show how these results apply to a wide class of crossed products of C*-algebras by actions of discrete groups. We also discuss an example where the hypothesis of our main theorem is not satisfied and the quantum symmetry group is not a generalised Drinfeld double.