Weyl groups of groupoid C*-algebras

TL;DR

This paper generalizes the concept of Weyl groups to groupoid C*-algebras, analyzes automorphism groups, and applies findings to various classes of C*-algebras, enriching the understanding of their symmetries.

Contribution

It introduces Weyl groups for groupoid C*-algebras, extending previous definitions, and studies their automorphism groups with applications to well-known C*-algebras.

Findings

Weyl groups are defined for groupoid C*-algebras.

Automorphism groups of these algebras are analyzed.

Applications to Cuntz, graph, and Deaconu-Renault C*-algebras are provided.

Abstract

In the theory of C*-algebras, the Weyl groups were defined for the Cuntz algebras and graph algebras by Cuntz and Conti et al. respectively. In this paper, we introduce and investigate the Weyl groups of groupoid C*-algebras as a natural generalization of the existing Weyl groups. Then we analyse several groups of automorphisms on groupoid C*-algebras. Finally, we apply our results to Cuntz algebras, graph algebras and C*-algebras associated with Deaconu-Renault systems.