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

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• Leavitt path algebras of separated graphs
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• Gauge-invariant ideals of C*-algebras of Boolean dynamical systems
• Contributions to the theory of C*-correspondences with applications to multivariable dynamics
• Strong Shift Equivalence in the C*-algebraic setting: Graphs and C*-correspondences
• Semicrossed products of the disc algebra
• C*-algebras associated with topological group quivers I: generators, relations and spatial structure
• Realising the Toeplitz algebra of a higher-rank graph as a Cuntz-Krieger algebra
• Strong Shift Equivalence of $C^{\ast }$-correspondences
• Morita equivalence of C*-correspondences passes to the related operator algebras
• Comparability in the graph monoid
• C*-algebras associated with topological group quivers II: K-groups
• C*-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras
• Semiprojectivity and properly infinite projections in graph C*-algebras
• A Note on the Gauge Invariant Uniqueness Theorem for C*-correspondences
• On graph algebras from interval maps
• Graded $K$-theory and $K$-homology of relative Cuntz-Pimsner algebras and graph $C^{\ast }$-algebras
• $C^{\ast }$-algebras associated to $C^{\ast }$-correspondences and applications to mirror quantum spheres