Passing $C^*$-correspondence Relations to the Cuntz-Pimsner algebras

TL;DR

This paper develops a functorial approach to relate $C^*$-correspondences with their Cuntz-Pimsner algebras, extending known Morita equivalence results to a broader class of correspondences.

Contribution

It constructs a functor from $C^*$-correspondences to Cuntz-Pimsner algebras, generalizing key Morita equivalence results in the theory.

Findings

Established a functorial mapping from correspondences to algebras

Extended Morita equivalence results to more general correspondences

Unified previous results under a common functorial framework

Abstract

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. Applications include a generalization of the well-known result of Muhly and Solel: Morita equivalent $C^*$-correspondences have Morita equivalent Cuntz-Pimsner algebras; as well as the result of Muhly, Pask, and Tomforde: regular strong shift equivalent $C^*$-correspondences have Morita equivalent Cuntz-Pimsner algebras.