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Simplicial Cohomology of Some Semigroup Algebras

Published online by Cambridge University Press:  20 November 2018

F. Gourdeau
Affiliation:
Département de Mathématiques et de Statistique, Université Laval, Cité Universitaire, QC e-mail: Frederic.Gourdeau@mat.ulaval.ca
A. Pourabbas
Affiliation:
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran e-mail: arpabbas@aut.ac.ir
M. C. White
Affiliation:
Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England e-mail: Michael.White@ncl.ac.uk
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Abstract

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In this paper, we investigate the higher simplicial cohomology groups of the convolution algebra ${{\ell }^{1}}\left( S \right)$ 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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2007

References

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