Biflatness and biprojectivity of the Fourier algebra

Details Biflatness and biprojectivity of the Fourier algebra Biflatness and biprojectivity of the Fourier algebra

2008-08-08

arxiv.org/abs/0808.1146v2

Arch. Math. (Basel) 92 (2009), 525-530

Mathematics

Functional Analysis

6 pages; a few typos fixed

Scientific paper

We show that the biflatness - in the sense of A. Ya. Helemskii - of the
Fourier algebra $A(G)$ of a locally compact group $G$ forces $G$ to either have
an abelian subgroup of finite index or to be non-amenable without containing
$F_2$, the free group in two generators, as a closed subgroup. An analogous
dichotomy is obtained for biprojectivity.

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