@article {
author = {Miri, Mohammad Reza and Nasrabadi, Ebrahim and Kazemi, Kianoush},
title = {Second Module Cohomology Group of Induced Semigroup Algebras},
journal = {Sahand Communications in Mathematical Analysis},
volume = {18},
number = {2},
pages = {73-84},
year = {2021},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2020.130935.826},
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 $n\in\mathbb{N}$, $\mathcal{H}_{\ell^1(E_{T})}^{2}(\ell^1(S_{T}),\ell^1(S_{T})^{(n)})$ is a Banach space, when $S$ is a commutative inverse semigroup.},
keywords = {second module cohomology group,inverse semigroup,induced semigroup,semigroup algebra},
url = {https://scma.maragheh.ac.ir/article_242308.html},
eprint = {https://scma.maragheh.ac.ir/article_242308_8206cd5c01689d1cfa1ad72adb684128.pdf}
}