On $C^{\ast }$-algebras associated with $C^{\ast }$-correspondences

Abstract

We study $C^{\ast }$-algebras arising from $C^{\ast }$-correspondences, which was introduced by the author. We prove the gauge-invariant uniqueness theorem, and obtain conditions for our $C^{\ast }$-algebras to be nuclear, exact, or satisfy the Universal Coefficient Theorem. We also obtain a 6-term exact sequence of $K$-groups involving the $K$-groups of our $C^{\ast }$-algebras.

29pages, some small changes

References in corpus (1)

• A construction of $C^{\ast }$-algebras from $C^{\ast }$-correspondences

Cited by in corpus (2)

• Adding tails to C*-correspondences
• A class of C^*-algebras generalizing both graph algebras and homeomorphism C^*-algebras I, fundamental results