Module cohomology group of inverse semigroup algebras

Document Type : Research Paper



Let $S$ be an inverse semigroup and let $E$ be its
subsemigroup of idempotents. In this paper we define the $n$-th
module cohomology group of Banach algebras and
show that the first module
cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is
zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$
we show that
$HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach space, for every odd $ninmathbb{N}$.