Product systems of C*-correspondences and Takai duality

TL;DR

This paper proves the Hao-Ng isomorphism for generalized gauge actions on product systems over abelian lattice orders and applies it to explore Takai duality, extending previous results in the field.

Contribution

It establishes the Hao-Ng isomorphism in a new setting and uses it to analyze Takai duality for these systems, generalizing prior work.

Findings

Hao-Ng isomorphism proven for generalized gauge actions

Takai duality explored in the context of product systems

Extension of Schafhauser's related results

Abstract

We establish the Hao-Ng isomorphism for generalized gauge actions of locally compact abelian groups on product systems over abelian lattice orders and we then use it to explore Takai duality in this context. As an application we generalize related work of Schafhauser.