Renault's Equivalence Theorem for Reduced Groupoid C*-algebras

TL;DR

This paper demonstrates that equivalent groupoids have Morita equivalent reduced C*-algebras using linking groupoids, extending the Equivalence Theorem to reduced C*-algebras in a natural way.

Contribution

It introduces a method to establish Morita equivalence of reduced C*-algebras for equivalent groupoids via linking groupoids, extending existing theorems.

Findings

Reduced C*-algebras of equivalent groupoids are Morita equivalent.

The Morita equivalence is compatible with the full groupoid C*-algebra equivalence.

Extension of the Equivalence Theorem to reduced C*-algebras.

Abstract

We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced C*-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid C*-algebras.