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- W4301016643 abstract "Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $mathbb{G}$ and 1-injectivity of $L^{infty}(widehat{mathbb{G}})$ as an operator $L^1(widehat{mathbb{G}})$-module. In particular, a locally compact group $G$ is amenable if and only if its group von Neumann algebra $VN(G)$ is 1-injective as an operator module over the Fourier algebra $A(G)$. As an application, we provide a decomposability result for completely bounded $L^1(widehat{mathbb{G}})$-module maps on $L^{infty}(widehat{mathbb{G}})$, and give a simplified proof that amenable discrete quantum groups have co-amenable compact duals which avoids the use of modular theory and the Powers--St{o}rmer inequality, suggesting that our homological techniques may yield a new approach to the open problem of duality between amenability and co-amenability." @default.
- W4301016643 created "2022-10-04" @default.
- W4301016643 creator A5088525336 @default.
- W4301016643 date "2015-07-12" @default.
- W4301016643 modified "2023-10-16" @default.
- W4301016643 title "Amenability and covariant injectivity of locally compact quantum groups II" @default.
- W4301016643 doi "https://doi.org/10.48550/arxiv.1507.03296" @default.
- W4301016643 hasPublicationYear "2015" @default.
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