First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras

‎Let S be a (not necessarily commutative) Clifford semigroup with idempotent set E. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of  semigroup algbera \ell^1(S) with coefficients in \ell^\infty(S) (and also  \ell^1(S)^{(2n-1)} for n\in \mathbb{N}) are equal.

First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras Keywords:

Clifford semigroup , Weak amenability , Weak module amenability , Cohomology group , Module cohomology group