On hereditary properties of quantum group amenability

Crann, Jason

doi:10.1090/proc/13365

On hereditary properties of quantum group amenability
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Proc. Amer. Math. Soc. 145 (2017), 627-635 Request permission

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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