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FELL BUNDLES AND IMPRIMITIVITY THEOREMS: MANSFIELD’S AND FELL’S THEOREMS

Part of: Selfadjoint operator algebras General theory of categories and functors Methods of category theory in functional analysis

Published online by Cambridge University Press:  07 June 2013

S. KALISZEWSKI ,
PAUL S. MUHLY ,
JOHN QUIGG  and
DANA P. WILLIAMS
S. KALISZEWSKI
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA email [email protected]
PAUL S. MUHLY
Affiliation:
Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA email [email protected]
JOHN QUIGG*
Affiliation:
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA email [email protected]
DANA P. WILLIAMS
Affiliation:
Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA email [email protected]
*
✉[email protected]
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Abstract

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In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel surjection of the first paper in the series to relate our version of Mansfield’s theorem to that of an Huef and Raeburn, and to give an automatic amenability result for certain transformation Fell bundles.

Keywords

imprimitivity theoremFell bundlegroupoid

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 46M15: Categories, functors 18A25: Functor categories, comma categories
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 95 , Issue 1 , August 2013 , pp. 68 - 75
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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