Simple nuclear C*-algebras not isomorphic to their opposites

Abstract

We show that it is consistent with Zermelo-Fraenkel set theory with the axiom of choice (ZFC) that there is a simple nuclear nonseparable [Formula: see text]-algebra, which is not isomorphic to its opposite algebra. We can furthermore guarantee that this example is an inductive limit of unital copies of the Cuntz algebra [Formula: see text] or of the canonical anticommutation relations (CAR) algebra.