A new look at crossed product correspondences and associated C*-algebras

TL;DR

This paper investigates the relationship between crossed product correspondences and their associated C*-algebras, extending known results to non-amenable groups and exploring implications at the Toeplitz algebra level.

Contribution

It provides a detailed analysis of the isomorphism between crossed product C*-correspondences and Cuntz-Pimsner algebras beyond the amenable group case, including Toeplitz algebras.

Findings

Extended the isomorphism results to non-amenable groups.

Analyzed the behavior of Toeplitz algebras under group actions.

Clarified the structure of crossed product correspondences.

Abstract

When a locally compact group acts on a C*-correspondence, it also acts on the associated Cuntz-Pimsner algebra in a natural way. Hao and Ng have shown that when the group is amenable the Cuntz-Pimsner algebra of the crossed product correspondence is isomorphic to the crossed product of the Cuntz-Pimsner algebra. In this paper, we have a closer look at this isomorphism in the case where the group is not necessarily amenable. We also consider what happens at the level of Toeplitz algebras.