Classification of Certain Infinite Simple C*-Algebras

Abstract

The class of C*-algebras, that arise as the crossed product of a stable simple AF-algebra with a Z-action determined by an automorphism, which maps a projection in the algebra onto a proper subprojection, is proved to consist of simple, purely infinite C*-algebras, and a specific subclass of it is proved to be classified by K-theory. This subclass is large enough to exhaust all possible K-groups: if G0 and G1 are countable abelian groups, with G1 torsion free (as it must be), then there is a C*-algebras A in the classified subclass with K0(A) ≅ G0 and K-1(A) ≅ G1. The subclass contains the Cuntz algebras O with n even, and the Cuntz-Krieger algebras OA, with K0(OA of finite old order, and it is closed under forming inductive limits. The C*-algebras in the classified subclass can be viewed as classifiable models (in a strong sense) of general, simple purely infinite C*-algebras with the same K-theory. © 1995 Academic Press. All rights reserved.