Amenability constants of central Fourier algebras of finite groups

John Sawatzky

paper

Amenability constants of central Fourier algebras of finite groups

arXiv:2210.16262

Abstract

We consider amenability constants of the central Fourier algebra $Z A (G)$ of a finite group $G$ . This is a dual object to $Z L^{1} (G)$ in the sense of hypergroup algebras, and as such shares similar amenability theory. We will provide several classes of groups where $A M (Z A (G)) = A M (Z L^{1} (G))$ , and discuss $A M (Z A (G))$ when $G$ has two conjugacy class sizes. We also produce a new counterexample that shows that unlike $A M (Z L^{1} (G))$ , $A M (Z A (G))$ does not respect quotient groups, however the class of groups that does has $\frac{7}{4}$ as the sharp amenability constant bound.