The cyclic and simplicial cohomology of $l^1(\mathbf {N})$
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- by Frédéric Gourdeau, B. E. Johnson and Michael C. White PDF
- Trans. Amer. Math. Soc. 357 (2005), 5097-5113 Request permission
Abstract:
Let $\mathcal {A}=l^1(\mathbf Z_+)$ be the unital semigroup algebra of $\mathbf N$. We show that the cyclic cohomology groups $\mathcal {H}C^n(\mathcal {A},\mathcal {A}’)$ vanish when $n$ is odd and are one dimensional when $n$ is even ($n\ge 2$). Using Connes’ exact sequence, these results are used to show that the simplicial cohomology groups $\mathcal {H}^n(\mathcal {A},\mathcal {A}’)$ vanish for $n\ge 2$. The results obtained are extended to unital algebras $l^1(S)$ for some other semigroups of $\mathbf {R}$.References
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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
- B. E. Johnson
- Affiliation: Department of Mathematics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, England
- 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): November 14, 2002
- Received by editor(s) in revised form: April 8, 2004
- Published electronically: April 13, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 5097-5113
- MSC (2000): Primary 46H20, 46J40; Secondary 43A20, 16E40
- DOI: https://doi.org/10.1090/S0002-9947-05-03702-5
- MathSciNet review: 2165399