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

Abstract

We study the ideal structure of $C^{\ast }$-algebras arising from $C^{\ast }$-correspondences. We prove that gauge-invariant ideals of our $C^{\ast }$-algebras are parameterized by certain pairs of ideals of original $C^{\ast }$-algebras. We show that our $C^{\ast }$-algebras have a nice property which should be possessed by generalization of crossed products. Applications to crossed products by Hilbert $C^{\ast }$-bimodules and relative Cuntz-Pimsner algebras are also discussed.

34 pages

References in corpus (3)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences
• The C*-algebras of arbitrary graphs
• C^*-algebras generated by scaling elements

Cited by in corpus (9)

• Adding tails to C*-correspondences
• Cuntz-Pimsner algebras for subproduct systems
• Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
• Crossed products by endomorphisms of $C_0(X)$-algebras
• Gauge-invariant ideals of C*-algebras of Boolean dynamical systems
• Simple Cuntz-Pimsner rings
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras II, examples
• A Cuntz-Pimsner Model for the $C^{\ast }$-algebra of a Graph of Groups
• KMS states on finite-graph C*-algebras