Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - ZL-amenability and characters for the group algebras of restricted direct products of finite groups
AU - Alaghmandan, Mahmood
AU - Choi, Yemon
AU - Samei, Ebrahim
PY - 2014/3/1
Y1 - 2014/3/1
N2 - 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.
AB - 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.
U2 - 10.1016/j.jmaa.2013.09.030
DO - 10.1016/j.jmaa.2013.09.030
M3 - Journal article
VL - 411
SP - 314
EP - 328
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -