Towards a classification of unitary elements of C*-algebras

2023/04/04 by Cantier, Laurent
#FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2304.01761

Abstract

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both domain and codomain of the functor Cu. We also tackle the classification beyond the AF case and more particularly, we look at unitary elements of what we call AH₁-algebras. We obtain positive progress as far as the existence part is concerned. Nevertheless, we reveal that extra information is needed for the uniqueness part of the classification that the Cuntz semigroup fails to capture.

Related

• The unitary Cuntz semigroup on the classification of non-simple\n C*-algebras
• Three Applications of the Cuntz Semigroup
• A total Cuntz semigroup for C^*-algebras of stable rank one
• The Cuntz semigroup of unital commutative AI-algebras
• Distinguishing C*-algebras by their unitary groups