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

Alaghmandan, Mahmood and Choi, Yemon and Samei, Ebrahim (2014) ZL-amenability and characters for the group algebras of restricted direct products of finite groups. Journal of Mathematical Analysis and Applications, 411 (1). pp. 314-328. ISSN 0022-247X

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.