Fourier algebra of a compact Lie group

TL;DR

This paper characterizes the weak amenability of the Fourier algebra of a compact connected Lie group, showing it holds if and only if the group is abelian, thus linking algebraic structure to harmonic analysis properties.

Contribution

It establishes a precise criterion for the weak amenability of Fourier algebras on compact Lie groups, connecting group structure with harmonic analysis.

Findings

A(G) is weakly amenable if and only if G is abelian.

Provides a complete characterization of weak amenability for Fourier algebras on compact connected Lie groups.

Highlights the deep connection between the algebraic structure of G and harmonic analysis properties.

Abstract

Let G be a compact connected Lie group. We prove that the Fourier algebra A(G) is weakly amenable if and only if G is abelian.