2n-Weak module amenability of semigroup algebras

Abstract. Let S be an inverse semigroup with the set of idempotents E. We prove that the semigroup algebra ℓ1(S) is always 2n-weakly module amenable as an ℓ1(E)-module, for any n ∈ N, where E acts on S trivially from the left and by multiplication from the right. Our proof is based on a common fixed point property for semigroups.