Second Module Cohomology Group of Induced Semigroup Algebras
Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)Publication Date: 2021-05-01
Authors : Mohammad Reza Miri; Ebrahim Nasrabadi; Kianoush Kazemi;
Page : 73-84
Keywords : second module cohomology group; inverse semigroup; induced semigroup; semigroup algebra;
Abstract
For a discrete semigroup $ S $ and a left multiplier operator $T$ on $S$, there is a new induced semigroup $S_{T}$, related to $S$ and $T$. In this paper, we show that if $T$ is multiplier and bijective, then the second module cohomology groups $mathcal{H}_{ell^1(E)}^{2}(ell^1(S), ell^{infty}(S))$ and $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1({S_{T}}), ell^{infty}(S_{T}))$ are equal, where $E$ and $E_{T}$ are subsemigroups of idempotent elements in $S$ and $S_{T}$, respectively. Finally, we show thet, for every odd $ninmathbb{N}$, $mathcal{H}_{ell^1(E_{T})}^{2}(ell^1(S_{T}),ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.
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Last modified: 2021-11-03 14:32:34