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 $ninmathbb{N}$.
Nasrabadi, E., & Pourabbas, A. (2011). Module cohomology group of inverse semigroup algebras. Bulletin of the Iranian Mathematical Society, 37(No. 4), 157-169.
MLA
E. Nasrabadi; A. Pourabbas. "Module cohomology group of inverse semigroup algebras". Bulletin of the Iranian Mathematical Society, 37, No. 4, 2011, 157-169.
HARVARD
Nasrabadi, E., Pourabbas, A. (2011). 'Module cohomology group of inverse semigroup algebras', Bulletin of the Iranian Mathematical Society, 37(No. 4), pp. 157-169.
VANCOUVER
Nasrabadi, E., Pourabbas, A. Module cohomology group of inverse semigroup algebras. Bulletin of the Iranian Mathematical Society, 2011; 37(No. 4): 157-169.