First cohomology on weighted semigroup algebras

Abstract

The aim of this work is to generalize Johnson's techniques in order to apply them to establish a bijective correspondence between $S$-derivations and continuous derivations on $M_a(S,ω),$ where $S$ is a locally compact foundation semigroup with identity $e$, and $ω$ is a weight function on $S$, and apply it to find a necessary condition for amenability of weighted group algebras.