Central Beurling algebras: Weak amenability of the central Beurling algebras on [FC]${}^{-}$ groups

Abstract

We study weak amenability of central Beurling algebras $Z{L}^1(G,\omega )$. The investigation is a natural extension of the known work on the commutative Beurling algebra $L^1(G,\omega )$. For [FC]${}^{-}$ groups we establish a necessary condition and for [FD]${}^{-}$ groups we give sufficient conditions for the weak amenability of $Z\L1o$. For a compactly generated [FC]${}^{-}$ group with the polynomial weight ${\omega }_{\alpha }(x)=(1+|x|{)}^{\alpha }$, we prove that $Z{L}^1(G,{\omega }_{\alpha })$ is weakly amenable if and only if $\alpha <1/2$.

To appear in the Michigan Math J

References in corpus (1)

• Non-weakly amenable Beurling algebras