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 G 0 and G 1 are countable abelian groups, with G 1 torsion free (as it must be), then there is a C*-algebras A in the classified subclass with K 0( A) ≅ G 0 and K -1( A) ≅ G 1. The subclass contains the Cuntz algebras O with n even, and the Cuntz-Krieger algebras O A , with K 0( O A 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.