A simple C*-algebra with a finite and an infinite projection

Details A simple C*-algebra with a finite and an infinite projection A simple C*-algebra with a finite and an infinite projection

2002-04-29

arxiv.org/abs/math/0204339v2

Acta Math. 191 (2003), 109-142

Mathematics

Operator Algebras

Revised version (contains a nuclear example), revised again August 2002

Scientific paper

An example is given of a simple, unital C*-algebra which contains an infinite and a non-zero finite projection. This C*-algebra is also an example of an infinite simple C*-algebra which is not purely infinite. A corner of this C*-algebra is a finite, simple, unital C*-algebra which is not stably finite. Our example shows that the type decomposition for von Neumann factors does not carry over to simple C*-algebras. Added March 2002: We also give an example of a simple, separable, nuclear C*-algebra in the UCT class which contains an infinite and a non-zero finite projection. This nuclear C*-algebra arises as a crossed product of an inductive limit of type I C*-algebras by an action of the integers.

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