RT journal article
T1 The groupoids of adaptable separated graphs and their type semigroups
A1 Ara, Pere
A1 Bosa, Joan
A1 Pardo Espino, Enrique
A1 Sims, Aidan
A2 Matemáticas
K1 Steinberg algebra
K1 Refinement monoid
K1 Type semigroup
AB 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.
PB arxiv.org
YR 2019
FD 2019-04-10
LK http://hdl.handle.net/10498/21186
UL http://hdl.handle.net/10498/21186
LA eng
NO 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.
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026