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arXiv · 1110.6683

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

Mahmood Alaghmandan·Yemon Choi·Ebrahim Samei
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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.

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Mahmood Alaghmandan, Yemon Choi, Ebrahim Samei. 2013-09-24. ZL-amenability and characters for the restricted direct products of finite groups. https://doi.org/10.1016/j.jmaa.2013.09.030

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