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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Vanishing of the third simplicial cohomology group of $l^1(\mathbf {Z}_+)$
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by Frédéric Gourdeau and Michael C. White PDF
Trans. Amer. Math. Soc. 353 (2001), 2003-2017 Request permission

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
  • Received by editor(s): September 27, 1999
  • Published electronically: January 3, 2001
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 2003-2017
  • MSC (2000): Primary 46H20, 46J40; Secondary 43A20, 16E40
  • DOI: https://doi.org/10.1090/S0002-9947-01-02738-6
  • MathSciNet review: 1813605