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Semi-étale groupoids and applications

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  • Department of Mathematical Sciences
We associate a C * -algebra to a locally compact Hausdorff groupoid with the property that the range map is locally injective. The construction generalizes J. Renault’s reduced groupoid C * -algebra of an étale groupoid and has the advantage that it works for the groupoid arising from a locally injective dynamical system by the method introduced in increasing generality by Renault, Deaconu and Anantharaman-Delaroche. We study the C * -algebras of such groupoids and give necessary and sufficient conditions for simplicity, and show that many of them contain a Cartan subalgebra as defined by Renault. In particular, this holds when the dynamical system is a shift space, in which case the C * -algebra coincides with the one introduced by Matsumoto and Carlsen.
Original languageEnglish
JournalAnnales de l'Institut Fourier
Volume60
Issue3
Pages (from-to)759-800
Number of pages41
ISSN0373-0956
Publication statusPublished - 2010

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