Amenability constants of central Fourier algebras of finite groups
Tom 174 / 2023
Streszczenie
We consider amenability constants of the central Fourier algebra of a finite group G. This is a dual object to ZL^1(G) in the sense of hypergroup algebras, and as such shares similar amenability theory. We provide several classes of groups where \mathrm{AM}(ZA(G)) = \mathrm{AM}(ZL^1(G)), and discuss \mathrm{AM}({ZA}(G)) when G has two conjugacy class sizes. We also produce a new counterexample which shows that unlike \mathrm{AM}({ZL}^1(G)), \mathrm{AM}({ZA}(G)) does not respect quotient groups, but the class of groups that it does has \frac {7}{4} as the sharp amenability constant bound.