Module and Hochschild cohomology of certain semigroup algebras

We study the relation between module and Hochschild cohomology groups of Banach algebras with a compatible module structure. More precisely, we show that for every commutative Banach \mathcal{A} - \mathfrak{A}-bimodule X and every k \in \mathbb{N}, the seminormed spaces \mathcal{H}^{k}_{\mathfrak{A}} (\mathcal{A},X^*) and $ \mathcal{H}^k (\frac{\mathcal{A}}{J},... Show more