Some examples of factor groupoids

TL;DR

This paper explores specific classes of Hausdorff étale factor groupoids derived from AF-groupoids and Cantor minimal systems, analyzing their C*-algebras and classifying them via K-theory and traces.

Contribution

It introduces new examples of factor groupoids and provides their K-theoretic and trace classifications within the Elliott scheme.

Findings

Reduced C*-algebras are classifiable in the Elliott scheme

K-theory and traces of these C*-algebras are explicitly described

Examples include quotients of AF-groupoids and nonhomogeneous extensions of Cantor systems

Abstract

We examine two classes of examples of Hausdorff \'etale factor groupoids; one comes from taking a quotient space of the unit space of an AF-groupoid, and the other comes from certain nonhomogeneous extensions of Cantor minimal systems considered by Robin Deeley, Ian Putnam, and Karen Strung. The reduced C$^*$-algebras of the factor groupoids are classifiable in the Elliott scheme, and we describe their $K$-theory and traces.