# 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}
}
• P. Ara
• Published 10 April 2019
• Mathematics
• International Mathematics Research Notices
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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We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and
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