Canad. Math. Bull. 57(2014), 449-462
Printed: Sep 2014
We calculate the exact amenability constant of the centre of
$\ell^1(G)$ when $G$ is one of the following classes of finite group:
dihedral; extraspecial; or Frobenius with abelian complement and
kernel. This is done using a formula which applies to all finite
groups with two character degrees. In passing, we answer in the
negative a question raised in work of the third author with Azimifard
and Spronk (J. Funct. Anal. 2009).
center of group algebras, characters, character degrees, amenability constant, Frobenius group, extraspecial groups
43A20 - $L^1$-algebras on groups, semigroups, etc.
20C15 - Ordinary representations and characters