Pure states on free group C*-algebras

TL;DR

This paper proves that all pure states on the reduced C*-algebra of a free group with uncountably many generators are equivalent under *-automorphisms, revealing a high level of symmetry in these states.

Contribution

It establishes the automorphism equivalence of all pure states on the reduced C*-algebra of a free group with uncountably many generators, a novel result in operator algebra theory.

Findings

All pure states are *-automorphism equivalent.

Implications for the structure of free group C*-algebras.

Insights into symmetry properties of pure states.

Abstract

We prove that all of the pure states of the reduced C*-algebra of the free goup on $\aleph_1$ generators are *-automorphism equivalent and extract some consequences of that fact.