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On a simple unital projectionless C*-algebra
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 121, Number 2, April 1999
- pp. 359-413
- 10.1353/ajm.1999.0012
- Article
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We construct a unital separable C*-algebra Z as an analog of the hyperfinite type II1 factor. Besides being nuclear, simple, projectionless, and infinite-dimensional, Z has a unique tracial state, and is KK-equivalent to [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /], the algebra of complex numbers. It is shown that unital endomorphisms on Z are approximately inner, and that Z is isomorphic to the infinite tensor product of its replicas. It is also shown that A ≅ Z ⊗ A for certain interesting classes of unital simple nuclear C*-algebras A of real rank zero.