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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Vanishing of the third simplicial cohomology group of $l^1(\mathbf{Z}_+)$


Authors: Frédéric Gourdeau and Michael C. White
Journal: Trans. Amer. Math. Soc. 353 (2001), 2003-2017
MSC (2000): Primary 46H20, 46J40; Secondary 43A20, 16E40
Published electronically: January 3, 2001
MathSciNet review: 1813605
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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 $\mathcal{H}C^3(\mathcal{I},\mathcal{I}')=0$.


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Additional Information

Frédéric Gourdeau
Affiliation: Département de Mathématiques et de Statistique, Université Laval, Cité Universitaire, Québec, Canada G1K 7P4
Email: Frederic.Gourdeau@mat.ulaval.ca

Michael C. White
Affiliation: Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England
Email: Michael.White@ncl.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02738-6
PII: S 0002-9947(01)02738-6
Keywords: Cohomology, Banach algebra
Received by editor(s): September 27, 1999
Published electronically: January 3, 2001
Article copyright: © Copyright 2001 American Mathematical Society