# Renault's equivalence theorem for reduced groupoid c*-algebras

@article{Sims2010RenaultsET, title={Renault's equivalence theorem for reduced groupoid c*-algebras}, author={Aidan Sims and Dana P. Williams}, journal={arXiv: Operator Algebras}, year={2010}, pages={223-239} }

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. r (H) are Morita equivalent via a quotient Xr of X (Theorem 17). Moreover, we show that the Rieffel correspondence associated to X matches up the kernel IC� r(G) of the canonical surjection of C � (G) onto C � (G) with the kernel ICr(H) of the surjection of C…

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