Homogeneity of the pure state space of a separable C*-algebra

TL;DR

This paper proves that for all separable simple C*-algebras, the pure state space is homogeneous under automorphisms, extending earlier results from UHF algebras to a broader class.

Contribution

It generalizes the homogeneity of pure state spaces from UHF algebras to all separable simple C*-algebras, using automorphism groups.

Findings

Pure state space is homogeneous under automorphisms for all separable simple C*-algebras.

Extends Powers' result from UHF algebras to a wider class.

Homogeneity holds under the subgroup of asymptotically inner automorphisms.

Abstract

We prove that the pure state space is homogeneous under the action of the automorphism group (or the subgroup of asymptotically inner automorphisms) for all the separable simple C*-algebras. The first result of this kind was shown by Powers for the UHF algebras some 30 years ago.