Amenability properties of the centres of group algebras

Azimifard, Ahmadreza; Samei, Ebrahim; Spronk, Nico

Amenability properties of the centres of group algebras

Authors

Azimifard, Ahmadreza

Samei, Ebrahim

Spronk, Nico

Description

Let G be a locally compact group, and ZL1(G) be the centre of its group algebra. We show that when $G$ is compact ZL1(G) is not amenable when G is either nonabelian and connected, or is a product of infinitely many finite nonabelian groups. We also, study, for some non-compact groups G, some conditions which imply amenability and hyper-Tauberian property, for ZL1(G).
20 pages