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

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<mark>Journal publication date</mark>1/03/2014
<mark>Journal</mark>Journal of Mathematical Analysis and Applications
Issue number1
Volume411
Number of pages15
Pages (from-to)314-328
Publication StatusPublished
<mark>Original language</mark>English

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.