Relatively compact sets in the reduced $C^{\ast}$-algebras of Coxeter groups

TL;DR

This paper characterizes relatively compact sets in the reduced $C^{*}$-algebras of finitely generated Coxeter groups through a geometrically defined positive semigroup, advancing understanding of their algebraic structure.

Contribution

It introduces a geometric approach to identify relatively compact sets in the reduced $C^{*}$-algebras of Coxeter groups, which is a novel method in this context.

Findings

Relatively compact sets are characterized via a positive semigroup.

The approach links geometric properties with algebraic compactness.

Provides new tools for analyzing Coxeter group $C^{*}$-algebras.

Abstract

We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.