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On hereditary properties of quantum group amenability


Author: Jason Crann
Journal: Proc. Amer. Math. Soc. 145 (2017), 627-635
MSC (2010): Primary 46M10, 43A07; Secondary 47L25, 46L89
DOI: https://doi.org/10.1090/proc/13365
Published electronically: October 18, 2016
MathSciNet review: 3577866
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Abstract: Given a locally compact quantum group $ \mathbb{G}$ and a closed quantum subgroup $ \mathbb{H}$, we show that $ \mathbb{G}$ is amenable if and only if $ \mathbb{H}$ is amenable and $ \mathbb{G}$ acts amenably on the quantum homogenous space $ \mathbb{G}/\mathbb{H}$. We also study the existence of $ L^1(\widehat {\mathbb{G}})$-module projections from $ L^{\infty }(\widehat {\mathbb{G}})$ onto $ L^{\infty }(\widehat {\mathbb{H}})$.


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Jason Crann
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: jcrann@math.carleton.ca

DOI: https://doi.org/10.1090/proc/13365
Keywords: Locally compact quantum groups, amenability
Received by editor(s): March 11, 2016
Published electronically: October 18, 2016
Communicated by: Adrian Ioana
Article copyright: © Copyright 2016 American Mathematical Society