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# Simplicial Cohomology of Some Semigroup Algebras

Published:2007-03-01
Printed: Mar 2007
• F. Gourdeau
• A. Pourabbas
• M. C. White
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## Abstract

In this paper, we investigate the higher simplicial cohomology groups of the convolution algebra $\ell^1(S)$ for various semigroups $S$. The classes of semigroups considered are semilattices, Clifford semigroups, regular Rees semigroups and the additive semigroups of integers greater than $a$ for some integer $a$. Our results are of two types: in some cases, we show that some cohomology groups are $0$, while in some other cases, we show that some cohomology groups are Banach spaces.
 Keywords: simplicial cohomology, semigroup algebra
 MSC Classifications: 43A20 - $L^1$-algebras on groups, semigroups, etc.