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Induction for locally compact quantum groups revisited

Part of: Selfadjoint operator algebras Locally compact groups and their algebras Linear algebraic groups and related topics

Published online by Cambridge University Press:  29 January 2019

Mehrdad Kalantar ,
Paweł Kasprzak ,
Adam Skalski  and
Piotr M. Sołtan
Mehrdad Kalantar
Affiliation:
Department of Mathematics, University of Houston, Houston, TX77204, USA (kalantar@math.uh.edu)
Paweł Kasprzak
Affiliation:
Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland (pawel.kasprzak@fuw.edu.pl)
Adam Skalski
Affiliation:
Institute of Mathematics of the Polish Academy of Sciences ul. Śniadeckich 8, 00-656Warszawa, Poland (a.skalski@impan.pl)
Piotr M. Sołtan
Affiliation:
Department of Mathematical Methods in Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland (piotr.soltan@fuw.edu.pl)
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Abstract

In this paper, we revisit the theory of induced representations in the setting of locally compact quantum groups. In the case of induction from open quantum subgroups, we show that constructions of Kustermans and Vaes are equivalent to the classical, and much simpler, construction of Rieffel. We also prove in general setting the continuity of induction in the sense of Vaes with respect to weak containment.

Keywords

Locally compact quantum groupinduction of representations

MSC classification

Primary: 22D30: Induced representations 46L89: Other “noncommutative” mathematics based on $C^*$-algebra theory
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations 20G42: Quantum groups (quantized function algebras) and their representations
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 2 , April 2020 , pp. 1071 - 1093
Copyright
Copyright © Royal Society of Edinburgh 2019

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