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Vanishing of the third simplicial cohomology group of

Authors:	Fré dé ric Gourdeau Michael C White

Institution:	Département de Mathématiques et de Statistique, Université Laval, Cité Universitaire, Québec, Canada G1K 7P4 ; Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England

Abstract:	We show that $\mathcal{H}^3(l^1(\mathbf{Z}_+),l^1(\mathbf{Z}_+)')=0$ . We first use the Connes-Tzygan exact sequence to prove that this is equivalent to the vanishing of the third cyclic cohomology group $\mathcal{H}C^3(\mathcal{I},\mathcal{I}')$ , where $\mathcal{I}$ is the non-unital Banach algebra $l^1(\mathbf{N})$ , and then prove that $\mathcal{H}C^3(\mathcal{I},\mathcal{I}')=0$ .

Keywords:	Cohomology Banach algebra

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