|Dept.||University of Waterloo|
Let G be a compact group and ZA(G) be the “central Fourier algebra”, i.e. the algebra of those u in A(G) for which u(x)=(yxy-1) for each x,y in G. I will discuss amenability and weak amenability for this algebra. The latter property holds exactly when G admits no connected non-abelian subgroups. For virtually abelian G, ZA(G) is amenable. I will present evidence for the converse, in particular infinite products of finite groups.
This represents joint work with M. Alaghmandan.