Pseudo-amenability of certain semigroup algebras (Q637608)

Let \(S\) be an inverse semigroup with uniformly locally finite idempotent set. \textit{F. Ghahramani} and \textit{Y. Zhang} [Math. Proc. Camb. Philos. Soc. 142, No. 1, 111--123 (2007; Zbl 1118.46046)] introduced and studied the notion of pseudo-amenability. In the paper under review, the authors investigate the pseudo-amenability of a semigroup algebra \(\ell^1(S)\) obtaining its equivalence with the amenability of the maximal subgroups of \(S\). As a particular case, they characterize the pseudo-amenability of Brandt semigroup algebras, showing that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of \(\ell ^{1}(S)\) is equivalent to the amenability of \(G\). This characterization of the pseudo-amenability of Brandt semigroup algebras answers a question raised in [\textit{M. M. Sadr}, Commentat. Math. Univ. Carol. 50, No. 3, 413--419 (2009; Zbl 1212.43003)].