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dc.contributor.authorAra, Pere
dc.contributor.authorBosa, Joan
dc.contributor.authorPardo, E.
dc.contributor.authorSims, Aidan
dc.contributor.otherMatemáticasen_US
dc.date.accessioned2019-04-11T11:01:53Z
dc.date.available2019-04-11T11:01:53Z
dc.date.issued2019-04-10
dc.identifier.urihttp://hdl.handle.net/10498/21186
dc.description.abstractGiven 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.en_US
dc.description.sponsorshipThe 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.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherarxiv.orgen_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectSteinberg algebraen_US
dc.subjectRefinement monoiden_US
dc.subjectType semigroupen_US
dc.titleThe groupoids of adaptable separated graphs and their type semigroupsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessen_US


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