2n-Weak module amenability of semigroup algebras

TL;DR

This paper proves that for any inverse semigroup, its semigroup algebra is always 2n-weakly module amenable as an (E)-module, regardless of n, expanding understanding of algebraic properties in semigroup theory.

Contribution

It establishes the 2n-weak module amenability of semigroup algebras for inverse semigroups, a novel generalization in the study of algebraic amenability.

Findings

Semigroup algebra (S) is 2n-weakly module amenable for all n.

The result holds for inverse semigroups with E acting trivially from the left.

The proof applies to any natural number n, showing a broad generalization.

Abstract

Let $S$ be an inverse semigroup with the set of idempotents $E$. We prove that the semigroup algebra $\ell^{1}(S)$ is always $2n$-weakly module amenable as an $\ell^{1}(E)$-module, for any $n\in \mathbb{N}$, where $E$ acts on $S$ trivially from the left and by multiplication from the right.