Strict comparison for twisted group C*-algebras
Operator Algebras
2026-04-28 v3 Group Theory
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.
Keywords
Cite
@article{arxiv.2505.18569,
title = {Strict comparison for twisted group C*-algebras},
author = {Sven Raum and Hannes Thiel and Eduard Vilalta},
journal= {arXiv preprint arXiv:2505.18569},
year = {2026}
}
Comments
7 pages; v3 included references to more recent results, minor modifications; v2 generalized from finitely generated to countable groups