A simple C*-algebra with a finite and an infinite projection
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.
Keywords
Cite
@article{arxiv.math/0204339,
title = {A simple C*-algebra with a finite and an infinite projection},
author = {Mikael Rordam},
journal= {arXiv preprint arXiv:math/0204339},
year = {2010}
}
Comments
Revised version (contains a nuclear example), revised again August 2002