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Amenability and covariant injectivity of locally compact quantum groups


Authors: Jason Crann and Matthias Neufang
Journal: Trans. Amer. Math. Soc. 368 (2016), 495-513
MSC (2010): Primary 22D15, 46L89, 81R15; Secondary 43A07, 46M10, 43A20
DOI: https://doi.org/10.1090/tran/6374
Published electronically: May 22, 2015
MathSciNet review: 3413871
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Abstract: As is well known, the equivalence between amenability of a locally compact group $ G$ and injectivity of its von Neumann algebra $ \mathcal {L}(G)$ does not hold in general beyond inner amenable groups. In this paper, we show that the equivalence persists for all locally compact groups if $ \mathcal {L}(G)$ is considered as a $ \mathcal {T}(L_2(G))$-module with respect to a natural action. In fact, we prove an appropriate version of this result for every locally compact quantum group.


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Additional Information

Jason Crann
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 – and – Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d’Ascq Cédex, France
Email: jason_crann@carleton.ca

Matthias Neufang
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 – and – Université Lille 1 - Sciences et Technologies, UFR de Mathématiques, Laboratoire de Mathématiques Paul Painlevé - UMR CNRS 8524, 59655 Villeneuve d’Ascq Cédex, France
Email: Matthias.Neufang@carleton.ca

DOI: https://doi.org/10.1090/tran/6374
Received by editor(s): April 15, 2013
Received by editor(s) in revised form: November 19, 2013
Published electronically: May 22, 2015
Article copyright: © Copyright 2015 American Mathematical Society