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Aidan Sims and Dana P. Williams
An equivalence theorem for reduced Fell bundle C*-algebras view print
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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 |
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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
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.
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| 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.
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| 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 03755-3551
dana.williams@Dartmouth.edu
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