-algebras and the tail-equivalence relation on Bratteli diagrams

Authors:
R. Exel and J. Renault

Journal:
Proc. Amer. Math. Soc. **134** (2006), 193-206

MSC (2000):
Primary 46L05, 46L85

Published electronically:
June 28, 2005

MathSciNet review:
2170559

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the -algebra associated to the tail-equivalence relation on a Bratteli diagram, according to a procedure recently introduced by the first-named author and A. Lopes, is isomorphic to the -algebra of the diagram. More generally we consider an approximately proper equivalence relation on a compact space for which the quotient maps are local homeomorphisms. We show that the algebra associated to under the above-mentioned procedure is isomorphic to the groupoid -algebra .

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Additional Information

**R. Exel**

Affiliation:
Departamento de Matemática, Universidade Federal de Santa Catarina, 88010-970 Florianópolis, Brasil

Email:
exel@mtm.ufsc.br

**J. Renault**

Affiliation:
Département de Mathématiques, Université d’Orléans, France

Email:
renault@labomath.univ-orleans.fr

DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08129-3

Received by editor(s):
April 26, 2004

Received by editor(s) in revised form:
August 24, 2004

Published electronically:
June 28, 2005

Additional Notes:
The first author was partially supported by CNPq

The second author was partially supported by Réseau pour les mathématiques, Coopération Franco-Brésilienne

Communicated by:
David R. Larson

Article copyright:
© Copyright 2005
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.