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Twisted crossed products by coactions

Part of: Selfadjoint operator algebras Locally compact groups and their algebras

Published online by Cambridge University Press:  09 April 2009

John Phillips  and
Iain Raeburn
John Phillips
Affiliation:
Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, B.C. V8W 3P4, Canada
Iain Raeburn
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle, New South Wales, 2308, Australia
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Abstract

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We consider coactions of a locally compact group G on a C*-algebra A, and the associated crossed product C*-algebra A× G. Given a normal subgroup N of G, we seek to decompose A× G as an iterated crossed product (A× G/ N) × N, and introduce notions of twisted coaction and twisted crossed product which make this possible. We then prove a duality theorem for these twisted crossed products, and discuss how our results might be used, especially when N is abelian.

MSC classification

Secondary: 46L55: Noncommutative dynamical systems 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations 22D35: Duality theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 3 , June 1994 , pp. 320 - 344
Copyright
Copyright © Australian Mathematical Society 1994

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