Semi etale groupoids and applications

TL;DR

This paper introduces a new class of locally compact Hausdorff groupoids, generalizing etale groupoids, and explores their associated C*-algebras, providing new criteria for simplicity and Cartan subalgebras, with applications to dynamical systems.

Contribution

It extends the theory of C*-algebras from etale groupoids to a broader class of groupoids, improving existing results and applying them to dynamical systems.

Findings

Generalized C*-algebra construction for new groupoid class

Established criteria for simplicity and Cartan subalgebras

Applied results to dynamical systems and subshifts

Abstract

We introduce a class of locally compact Hausdorff groupoids and show how to associate C*-algebras to them in a way which generalizes the reduced C*-algebra of an 'etale groupoid. Focusing on criteria for simplicity and existence of Cartan subalgebras, we obtain results which both generalize and improve on the corresponding results from the 'etale case. In the second part we apply the results to dynamical systems and subshifts.