Strict comparison for twisted group C*-algebras

TL;DR

This paper proves that certain twisted group C*-algebras of groups with rapid decay are selfless and have strict comparison, especially focusing on acylindrically hyperbolic groups.

Contribution

It establishes that reduced twisted group C*-algebras of selfless groups with rapid decay are selfless and have strict comparison, extending known properties to new classes of groups.

Findings

Twisted group C*-algebras of selfless groups with rapid decay are selfless.

Such algebras of acylindrically hyperbolic groups are pure and have strict comparison.

The results apply even when the groups have a nontrivial finite radical.

Abstract

We prove that any reduced twisted group C*-algebra of a selfless group with the rapid decay property is selfless. As an application, we show that twisted group C*-algebras of acylindrically hyperbolic groups (possibly with nontrivial finite radical) and rapid decay are pure, and hence have strict comparison.