## ZL-amenability and characters for the restricted direct products of finite groups

#### Authors

Mahmood Alaghmandan, Yemon Choi*, Ebrahim Samei

* Corresponding author

Keywords: Centre of group algebras, restricted direct product of finite groups, amenability, absolutely idempotent characters, maximal ideals.

MSC 2010: 43A20 (primary); 20C15 (secondary).

DOI: 10.1016/j.jmaa.2013.09.03

#### Status

Preprint version available at arXiv 1110.6683 (identical to accepted manuscript, modulo formatting and the correction of some typos).

#### Reviews

[ Math Reviews (summary) | Zentralblatt (summary) ]

#### Abstract

Let $G$ be a restricted direct product of finite groups $\{ G_i \}_{i\in I}$, and let $\Zl^1(G)$ denote the centre of its group algebra. We show that $\Zl^1(G)$ is amenable if and only if $G_i$ is abelian for all but finitely many $i$, and characterize the maximal ideals of $\Zl^1(G)$ which have bounded approximate identities. We also study when an algebra character of $\Zl^1(G)$ belongs to $c_0$ or $\ell^p$ and provide a variety of examples.