Title

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

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Link to publisher version (DOI)

http://dx.doi.org/10.1093/imrn/rnaa022