Weyl groups of groupoid C*-algebras

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.