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

Mikael Rordam

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arXiv · math/0204339

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

Mikael Rordam

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Abstract

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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BibTeX RIS

Mikael Rordam. 2002-08-28. A simple C*-algebra with a finite and an infinite projection. https://arxiv.org/abs/math/0204339

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