Introduction

We prove a classification theorem for simple direct limits of what we

call even Cuntz-circle algebras: finite direct sums of algebras of the form

C(X)®Mn®Om, where m is even, Om is the Cuntz algebra (first introduced

in [Cul]), and X is either a point, a compact interval, or the circle S

1

. The

unital version of our main theorem is:

T h e o r e m A. (Theorem 5.4) Let A = limA^ and B = limi?*. be simple

separable unital C*-algebras, which are direct limits of even Cuntz-circle

algebras. Assume that the homomorphisms Ak -» A and Bk — » B are

"approximately absorbing" (defined in Section 1). Then A = B if and only

if (Ko{A),[lA]J1(A)) ^ (K0(B),[lB],Ki(B)). In particular, if there are

isomorphisms a

0

: Ko(A) — KQ(B) and a\ : K\(A) -» K\(B) such that

^OQIA] )

=

[1B],

then A is isomorphic to B.

As a corollary, we obtain:

T h e o r e m B . (Corollary 5.12) Let 6\ and 92 be irrational numbers, and

let AQX and AQ2 be the corresponding irrational rotation algebras. Then for

any even m, we have Aex ® Om = l^2 ® Om.

This contrasts with the fact, due to Rieffel [Rf] and Pimsner and Voicu-

lescu [PV1] that A$1 = A^2 only when ^i = ±^

2

(mod Z). (Theorem B was

already known for m = 2 [Ln3], and remains unknown for odd m.) More

Received by the editor April 12, 1994

This research is partially supported by NSF grants DMS 93-01082 (H. Lin) and

DMS 91-06285 (N. C. Phillips). The results of this article were announced at the

January 1994 meeting of the American Mathematical Society.

1