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Subgroup Correspondences

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

Published online by Cambridge University Press:  14 August 2018

S. Kaliszewski ,
Nadia S. Larsen  and
John Quigg
S. Kaliszewski
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA (kaliszewski@asu.edu; quigg@asu.edu)
Nadia S. Larsen
Affiliation:
Department of Mathematics, University of Oslo, PO Box 1053 Blindern, N-0316 Oslo, Norway (nadiasl@math.uio.no)
John Quigg*
Affiliation:
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287, USA (kaliszewski@asu.edu; quigg@asu.edu)
*
*Corresponding author.
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Abstract

For a closed subgroup of a locally compact group the Rieffel induction process gives rise to a C*-correspondence over the C*-algebra of the subgroup. We study the associated Cuntz–Pimsner algebra and show that, by varying the subgroup to be open, compact, or discrete, there are connections with the Exel–Pardo correspondence arising from a cocycle, and also with graph algebras.

Keywords

C*-correspondencesCuntz–Pimsner algebrasgroup C*-algebras

MSC classification

Primary: 46L08: $C^*$-modules
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 4 , November 2018 , pp. 1127 - 1154
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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Footnotes

Dedicated to the memory of Ola Bratteli

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