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- W2276519751 abstract "We study various operator homological properties of the Fourier algebra $A(G)$ of a locally compact group $G$. Establishing the converse of two results of Ruan and Xu, we show that $A(G)$ is relatively operator 1-projective if and only if $G$ is IN, and that $A(G)$ is relatively operator 1-flat if and only if $G$ is inner amenable. We also exhibit a large class of groups for which $A(G)$ is not relatively operator $C$-flat for any $Cgeq1$. Along the way, we establish a hereditary property of inner amenability, and answer an open question of Lau and Paterson. In the bimodule setting, we show that relative operator 1-biflatness of $A(G)$ is equivalent to the existence of a contractive approximate diagonal in the Fourier--Stieltjes algebra $B(Gtimes G)$, thereby establishing the converse to a result of Aristov, Runde, and Spronk. We conjecture that relative 1-biflatness of $A(G)$ is equivalent to the existence of a quasi-central bounded approximate identity in $L^1(G)$, and verify the conjecture in many special cases. We finish with an application to the operator homology of $A_{cb}(G)$, giving examples of weakly amenable groups for which $A_{cb}(G)$ is not operator amenable." @default.
- W2276519751 created "2016-06-24" @default.
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- W2276519751 date "2016-02-17" @default.
- W2276519751 modified "2023-09-27" @default.
- W2276519751 title "On the operator homology of the Fourier algebra" @default.
- W2276519751 hasPublicationYear "2016" @default.
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