The Groupoids of Adaptable Separated Graphs and Their Type Semigroups
Publication Name
International Mathematics Research Notices
Abstract
Given an adaptable separated graph, we construct an associated groupoid and explore its type semigroup. Specifically, we first attach to each adaptable separated graph a corresponding semigroup, which we prove is an E?-unitary inverse semigroup. As a consequence, the tight groupoid of this semigroup is a Hausdorff étale groupoid. We show that this groupoid is always amenable and that the type semigroups of groupoids obtained from adaptable separated graphs in this way include all finitely generated conical refinement monoids. The first three named authors will utilize this construction in forthcoming work to solve the realization problem for von Neumann regular rings, in the finitely generated case.
Open Access Status
This publication may be available as open access
Volume
2021
Issue
20
First Page
15444
Last Page
15496