A Classification Result for Approximately Homogeneous C*-algebras of Real Rank Zero

Abstract.

We prove that the total K-theory group $\underline {K}(-) = \oplus_{n=0}^{\infty} K_*(-;\Bbb {Z}/n)$ equipped with a natural order structure and acted upon by the Bockstein operations is a complete invariant for a class of approximately subhomogeneous C*-algebras of real rank zero which include the inductive limits of systems of the form $P_{1} M_{n(1)} (C(X_{1})) P_{1} \longrightarrow P_{2} M_{n(2)} (C(X_{2})) P_{2} \longrightarrow \cdots$ where P _i are selfadjoint projections in M _{n ( i )}(C(X _i )) and X _i are finite (possibly disconnected) CW complexes whose dimensions satisfy a certain growth condition. The problem of finding suitable invariants for the study of C*-algebras of this type was proposed by Effros. Our result represents a substantial generalization of the classification theorem of approximately finite dimensional (AF) C*-algebras, due to Elliott.