Towards a classification of unitary elements of C*-algebras

Laurent Cantier

Published 2023-04-04Version 1

The classification of unitary elements of C*-algebras has started in [3], where the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We complete the proof by addressing the existence part of the conjecture. We also tackle the classification beyond the AF case and more particularly, we look at unitary elements of what we call AX-algebras. We obtain positive progress as far as the existence part is concern. Nevertheless, we reveal some crucial information needed for the uniqueness part of the classification that the Cuntz semigroup fails to capture.