# The Groupoids of Adaptable Separated Graphs and Their Type Semigroups

@article{Ara2019TheGO, title={The Groupoids of Adaptable Separated Graphs and Their Type Semigroups}, author={Pere Ara and Joan Bosa and Enrique Pardo and Aidan Sims}, journal={International Mathematics Research Notices}, year={2019} }

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…

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