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Second Module Cohomology Group of Induced Semigroup Algebras

Journal: Sahand Communications in Mathematical Analysis (Vol.18, No. 2)

Publication Date:

Authors : ; ; ;

Page : 73-84

Keywords : second module cohomology group‎; ‎inverse semigroup‎; ‎induced semigroup; semigroup algebra;

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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.

Last modified: 2021-11-03 14:32:34