A remark on invariants for C*-algebras of stable rank one

TL;DR

This paper demonstrates that for C*-algebras with stable rank one, the Cuntz and Thomsen semigroups are equivalent invariants, each determining the other in a natural manner.

Contribution

It establishes the equivalence of the Cuntz and Thomsen semigroups as invariants for stable rank one C*-algebras, clarifying their relationship.

Findings

Cuntz and Thomsen semigroups contain the same information

These invariants determine each other naturally

The result applies specifically to stable rank one C*-algebras

Abstract

It is shown that, for a C*-algebra of stable rank one (i.e., in which the invertible elements are dense), two well-known isomorphism invariants, the Cuntz semigroup and the Thomsen semigroup, contain the same information. More precisely, these two invariants, viewed appropiately, determine each other in a natural way.