@misc{10498/21186,
year = {2019},
month = {4},
url = {http://hdl.handle.net/10498/21186},
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 con- sequence, the tight groupoid of this semigroup is a Hausdorff  ́etale 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.},
organization = {The first, second and third authors were partially supported by the DGI-MINECO and European Regional Development Fund, jointly, through the grant MTM2017-83487-P. The first and second authors acknowledge support from the Spanish Ministry of Economy and Competitiveness, through the Mar ́ıa de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0445) and from the Generalitat de Catalunya through the grant 2017-SGR-1725. The third author was partially supported by PAI III grant FQM-298 of the Junta de Andaluc ́ıa. The fourth author was partially supported by the Australian Research Council grant DP150101595.},
publisher = {arxiv.org},
keywords = {Steinberg algebra},
keywords = {Refinement monoid},
keywords = {Type semigroup},
title = {The groupoids of adaptable separated graphs and their type semigroups},
author = {Ara, Pere and Bosa, Joan and Pardo Espino, Enrique and Sims, Aidan},
}