 

Aidan Sims and Dana P. Williams
An equivalence theorem for reduced Fell bundle C*algebras view print


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


Abstract
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
crosssectional algebra of L(E) contains those of B and C
as complementary full corners, and likewise for reduced
crosssectional algebras. We show how our results generalise to
groupoid crossedproducts the fact, proved by Quigg and Spielberg,
that Raeburn's symmetric imprimitivity theorem passes through the
quotient map to reduced crossed products.


Acknowledgements
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
asims@uow.edu.au
Dana P. Williams:
Department of Mathematics, Dartmouth College, Hanover, NH 037553551
dana.williams@Dartmouth.edu

