On a simple unital projectionless C*-algebra

摘要

We construct a unital separable C*-algebra Z as an analog of the hyperfinite type III factor. Besides being nuclear, simple, projectionless, and infinite-dimensional Z has a unique tracial state. and is KK-equivalent to C 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 congruent to Z x A for certain interesting classes of unital simple nuclear C*-algebras A of real rank zero. [References: 47]