CLASSIFICATION OF CERTAIN INFINITE SIMPLE C-ASTERISK-ALGEBRAS

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)congruent to G(0) and K-1(A)congruent to G(1). The subclass contains the Cuntz algebras O-n, 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. (C) 1995 Academic Press, Inc.