Journal of Operator Theory

Volume 68, Issue 1, Summer 2012 pp. 223-239.

Renault's equivalence theorem for reduced groupoid $C^*$-algebras

Authors: Aidan Sims (1) and Dana P. Williams (2)
Author institution: (1) School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia
(2) Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551, U.S.A.

Summary: We use the technology of linking groupoids to show that equivalent groupoids have Morita equivalent reduced $C^*$-algebras. This equivalence is compatible in a natural way in with the Equivalence Theorem for full groupoid $C^*$-algebras.

Keywords: Groupoid, groupoid equivalence, reduced $C^*$-algebra, equivalence theorem, Hilbert bimodule, $C^*$-correspondence, Morita equivalence, Haar system

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