Module super-amenability for semigroup algebras

Abstract

Let $S$ be an inverse semigroup with the set of idempotents $E$. In this paper we define the module super-amenability of a Banach algebra which is a Banach module over another Banach algebra with compatible actions, and show that when $E$ is upward directed and acts on $S$ trivially from left and by multiplication from right, the semigroup algebra ${\ell }^1(S)$ is ${\ell }^1(E)$-module super-amenable if and only if an appropriate group homomorphic image of $S$ is finite.

9 pages

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