Fell Bundles and Imprimitivity Theorems: Towards a Universal Generalized Fixed Point Algebra

We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product an...

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Bibliographic Details
Published in:Indiana University mathematics journal 2013-01, Vol.62 (6), p.1691-1716
Main Authors: Kaliszewski, S., Muhly, Paul S., Quigg, John, Williams, Dana P.
Format: Article
Language:English
Subjects:
Algebra
Automorphisms
College mathematics
Equivalence relation
Homomorphisms
Inner products
Linear transformations
Mathematical theorems
Quotients
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Summary:We apply the One-Sided Action Theorem from the first paper in this series to prove that Rieffel's Morita equivalence between the reduced crossed product by a proper saturated action and the generalized fixed-point algebra is a quotient of a Morita equivalence between the full crossed product and a "universal" fixed-point algebra. We give several applications to Fell bundles over groups, reduced crossed products as fixed-point algebras, and C*-bundles.
ISSN:0022-2518
1943-5258
DOI:10.1512/iumj.2013.62.5107