We prove a classification theorem for purely infinite simple C*-algebras that
is strong enough to show that the tensor products of two different irrational
rotation algebras with the same even Cuntz algebra are isomorphic. In more
detail, let C be the class of simple C*-algebras A which are direct limits
A = limAfc, in which each Ak is a finite direct sum of algebras of the form
C(X) ® Mn g 0
, where m is even, Om is the Cuntz algebra, and X is
either a point, a compact interval, or the circle 5
, and each map Ak A is
approximately absorbing. ("Approximately absorbing" is defined in Section
1.) We show that two unital C*-algebras A and B in C are isomorphic if and
only if
(KoiA^lUlKiiA)) ~ (K0(B),[lB],Kl(B)).
This class is large enough to exhaust all possible AT-groups: if Go and G\
are countable odd torsion (abelian) groups and g Go, then there is a C*-
algebra A in C with (K0{A), [lA], K\{A)) = (G0,#, G\). The class C contains
the tensor products of irrational rotation algebras with even Cuntz algebras.
It is also closed under the formation of hereditary subalgebras, countable
direct limits (provided that the direct limit is simple), and tensor products
with simple AF algebras.
Key Words: Even Cuntz-circle algebras, Classification of simple C*-algebras,
AT-theory, Direct limits.
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