First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras
Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 4)Publication Date: 2020-11-01
Authors : Ebrahim Nasrabadi;
Page : 39-47
Keywords : Clifford semigroup; Weak amenability; Weak module amenability; Cohomology group; Module cohomology group;
Abstract
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 $nin mathbb{N}$) are equal.
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