Invariant basis number and basis types for C*-algebras

Abstract

We develop the property of Invariant Basis Number (IBN) in the context of C*- algebras and their Hilbert modules. A complete K-theoretic characterization of C*- algebras with IBN is given. A scheme for classifying C*-algebras which do not have IBN is given and we prove that all such classes are realized. We investigate the invariance of IBN, or lack thereof, under common C-algebraic construction and perturbation techniques. Finally, applications of Invariant Basis Number to the study of C*-dynamical systems and the classification program are investigated.