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Extension problems and non-Abelian duality for C*-algebras

Published online by Cambridge University Press:  17 April 2009

Astrid an Huef ,
S. Kaliszewski  and
Iain Raeburn
Astrid an Huef
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, New South Wales 2052, Australia, e-mail: astrid@unsw.edu.au
S. Kaliszewski
Affiliation:
School of Mathematical and Physical Sciences, University of Newcastle, NSW 2308, Australia, e-mail: iain.raeburn@newcastle.edu.au
Iain Raeburn
Affiliation:
Department of Mathematics and Statistics, Arizona State University, AZ 85287–1804, United States of America, e-mail: kaliszewski@asu.edu
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Suppose that H is a closed subgroup of a locally compact group G. We show that a unitary representation U of H is the restriction of a unitary representation of G if and only if a dual representation Û of a crossed product C*(G) ⋊ (G/H) is regular in an appropriate sense. We then discuss the problem of deciding whether a given representation is regular; we believe that this problem will prove to be an interesting test question in non-Abelian duality for crossed products of C*-algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 229 - 238
Copyright
Copyright © Australian Mathematical Society 2007

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