An Infinite C*-algebra with a Dense, Stably Finite *-Subalgebra

Abstract

We construct a unital pre-C*-algebra $A_0$ which is stably finite, in the sense that every left invertible square matrix over $A_0$ is right invertible, while the C*-completion of $A_0$ contains a non-unitary isometry, and so it is infinite.

5 pages