Simplicial (Co)-homology of
| Autor: | Frédéric Gourdeau, Yasser Farhat |
|---|---|
| Rok vydání: | 2018 |
| Předmět: | |
| Zdroj: | Canadian Mathematical Bulletin. 62:756-766 |
| ISSN: | 1496-4287 0008-4395 |
| DOI: | 10.4153/s0008439518000644 |
| Popis: | We consider the unital Banach algebra$\ell ^{1}(\mathbb{Z}_{+})$and prove directly, without using cyclic cohomology, that the simplicial cohomology groups${\mathcal{H}}^{n}(\ell ^{1}(\mathbb{Z}_{+}),\ell ^{1}(\mathbb{Z}_{+})^{\ast })$vanish for all$n\geqslant 2$. This proceeds via the introduction of an explicit bounded linear operator which produces a contracting homotopy for$n\geqslant 2$. This construction is generalised to unital Banach algebras$\ell ^{1}({\mathcal{S}})$, where${\mathcal{S}}={\mathcal{G}}\cap \mathbb{R}_{+}$and${\mathcal{G}}$is a subgroup of $\mathbb{R}_{+}$. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|