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The uniform Roe algebra of an inverse semigroup

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dc.affiliation.dptoUC3M. Departamento de Matemáticases
dc.affiliation.grupoinvUC3M. Grupo de Investigación: Análisis Aplicadoes
dc.contributor.authorLledó Macau, Fernando
dc.contributor.authorMartinez, Diego
dc.contributor.funderMinisterio de Economía y Competitividad (España)es
dc.date.accessioned2023-09-11T13:27:30Z
dc.date.available2023-09-11T13:27:30Z
dc.date.issued2021-07-01
dc.description.abstractGiven a discrete and countable inverse semigroup S one can study, in analogy to the group case, its geometric aspects. In particular, we can equip S with a natural metric, given by the path metric in the disjoint union of its Schützenberger graphs. This graph, which we denote by ΛS, inherits much of the structure of S. In this article we compare the C*-algebra RS, generated by the left regular representation of S on 2(S) and ∞(S), with the uniform Roe algebra over the metric space, namely C∗u(ΛS). This yields a characterization of when RS = C∗u(ΛS), which generalizes finite generation of S. We have termed this by admitting a finite labeling (or being FL), since it holds when ΛS can be labeled in a finitary manner. The graph ΛS, and the FL condition, also allow to analyze large scale properties of ΛS and relate them with C*-properties of the uniform Roe algebra. In particular, we show that domain measurability of S (a notion generalizing Day’s definition of amenability of a semigroup, cf., [6]) is a quasi-isometric invariant of ΛS. Moreover, we characterize property A of ΛS (or of its components) in terms of the nuclearity and exactness of the corresponding C*-algebras. We also treat the special classes of F-inverse and E-unitary inverse semigroups from this large scale point of view.en
dc.description.sponsorshipSupported by research projects MTM2017-84098-P and Severo Ochoa SEV-2015-0554 of the Spanish Ministry of Economy and Competition (MINECO), Spain.en
dc.format.extent28
dc.identifier.bibliographicCitationLledó, F., & Martínez, D. (2021). The uniform roe algebra of an inverse semigroup. Journal of Mathematical Analysis and Applications, 499(1), 124996.en
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2021.124996
dc.identifier.issn0022-247X
dc.identifier.publicationfirstpage1
dc.identifier.publicationissue1, 124996
dc.identifier.publicationlastpage28
dc.identifier.publicationtitleJournal of Mathematical Analysis and Applicationsen
dc.identifier.publicationvolume499
dc.identifier.urihttps://hdl.handle.net/10016/38295
dc.identifier.uxxiAR/0000026848
dc.language.isoengen
dc.publisherElsevieren
dc.relation.projectIDGobierno de España. MTM2017-84098-Pes
dc.relation.projectIDGobierno de España. SEV-2015-0554es
dc.rights© 2021 Elsevier Inc.en
dc.rightsAtribución-NoComercial-SinDerivadas 3.0 España*
dc.rights.accessRightsopen accessen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/*
dc.subject.ecienciaMatemáticases
dc.subject.otherInverse semigroupen
dc.subject.otherSchützenberger graphen
dc.subject.otherUniform Roe algebraen
dc.subject.otherProperty aen
dc.titleThe uniform Roe algebra of an inverse semigroupen
dc.typeresearch article*
dc.type.hasVersionAM*
dspace.entity.typePublication
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