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arXiv · 1208.2986

Amenability and covariant injectivity of locally compact quantum groups

Jason Crann·Matthias Neufang
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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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Jason Crann, Matthias Neufang. 2012-08-14. Amenability and covariant injectivity of locally compact quantum groups. https://arxiv.org/abs/1208.2986

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