New York Journal of Mathematics
Volume 19 (2013) 159-178


Aidan Sims and Dana P. Williams

An equivalence theorem for reduced Fell bundle C*-algebras

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Published: May 24, 2013
Keywords: Fell bundle, groupoid, groupoid equivalence, reduced C*-algebra, equivalence theorem, Hilbert bimodule, C*-correspondence, Morita equivalence
Subject: 46L55

We show that if E is an equivalence of upper semicontinuous Fell bundles B and C over groupoids, then there is a linking bundle L(E) over the linking groupoid L such that the full cross-sectional algebra of L(E) contains those of B and C as complementary full corners, and likewise for reduced cross-sectional algebras. We show how our results generalise to groupoid crossed-products the fact, proved by Quigg and Spielberg, that Raeburn's symmetric imprimitivity theorem passes through the quotient map to reduced crossed products.


The second author was partially supported by a grant from the Simons Foundation. This research was partially supported by the Edward Shapiro Fund at Dartmouth College, and by the Australian Research Council.

Author information

Aidan Sims:
School of Mathematics and Applied Statistics, University of Wollongong, NSW 2522, Australia

Dana P. Williams:
Department of Mathematics, Dartmouth College, Hanover, NH 03755-3551