Adding tails to C*-correspondences

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.

24 pages, uses XY-pic. A few typos corrected, final version for publication

References in corpus (2)

• Ideal structure of $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences
• On $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences

Cited by in corpus (1)

• Strong Shift Equivalence in the C*-algebraic setting: Graphs and C*-correspondences