Adding tails to C*-correspondences

TL;DR

This paper introduces a method to add tails to C*-correspondences, extending techniques from graph C*-algebras to broader classes of C*-algebras, and proves a gauge-invariant uniqueness theorem.

Contribution

It generalizes the tail-adding process to C*-correspondences and applies it to extend results for augmented Cuntz-Pimsner algebras, including a new gauge-invariant uniqueness theorem.

Findings

Extended tail-adding technique to general C*-correspondences

Proved a gauge-invariant uniqueness theorem for these algebras

Defined relative graph C*-algebras and linked their properties to Cuntz-Pimsner algebras

Abstract

We describe a method of adding tails to C*-correspondences which generalizes the process used in the study of graph C*-algebras. We show how this technique can be used to extend results for augmented Cuntz-Pimsner algebras to C*-algebras associated to general C*-correspondences, and as an application we prove a gauge-invariant uniqueness theorem for these algebras. We also define a notion of relative graph C*-algebras and show that properties of these C*-algebras can provide insight and motivation for results about relative Cuntz-Pimsner algebras.