The Jiang–Su algebra revisited

Abstract

We give a number of new characterizations of the Jiang–Su algebra 𝒵, both intrinsic and extrinsic, in terms of C*-algebraic, dynamical, topological and K-theoretic conditions. Along the way we study divisibility properties of C*-algebras, we give a precise characterization of those unital C*-algebras of stable rank one that admit a unital embedding of the dimension-drop C*-algebra Zn, n+1, and we prove a cancellation theorem for the Cuntz semigroup of C*-algebras of stable rank one.