Semi-étale groupoids and applications

Klaus Thomsen[1]

  • [1] Institut for matematiske fag Ny Munkegade 8000 Aarhus C (Denmark)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 3, page 759-800
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Thomsen, Klaus. "Semi-étale groupoids and applications." Annales de l’institut Fourier 60.3 (2010): 759-800. <http://eudml.org/doc/116292>.

@article{Thomsen2010,
abstract = {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.},
affiliation = {Institut for matematiske fag Ny Munkegade 8000 Aarhus C (Denmark)},
author = {Thomsen, Klaus},
journal = {Annales de l’institut Fourier},
keywords = {Groupoids; $C^*$-algebras; dynamical systems; groupoids; -algebras},
language = {eng},
number = {3},
pages = {759-800},
publisher = {Association des Annales de l’institut Fourier},
title = {Semi-étale groupoids and applications},
url = {http://eudml.org/doc/116292},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Thomsen, Klaus
TI - Semi-étale groupoids and applications
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 3
SP - 759
EP - 800
AB - 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.
LA - eng
KW - Groupoids; $C^*$-algebras; dynamical systems; groupoids; -algebras
UR - http://eudml.org/doc/116292
ER -

References

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