Vanishing of the third simplicial cohomology group of \(\ell^1(\mathbf{Z}_+)\) (Q2701693)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Vanishing of the third simplicial cohomology group of \(\ell^1(\mathbf{Z}_+)\) |
scientific article |
Statements
19 February 2001
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Banach algebra
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third cyclic cohomology group
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0.8879754
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0.8846239
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0.87723345
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0.87195396
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0.86943096
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Vanishing of the third simplicial cohomology group of \(\ell^1(\mathbf{Z}_+)\) (English)
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The authors obtain the result announced in the title by proving that it is equivalent with vanishing of the third cyclic cohomology group \(HC^3(\ell_1(N),\ell_1(N)^-)\) and obtaining the latter result. For the second simplicial cohomology group the result was known earlier, and the general conjecture is that all these cohomologies vanish for \(n\geq 2\). The proof is quite involved.
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