CrossRef
Open Access
2018
Simplicial (Co)-homology of
Yasser Farhat
Frédéric Gourdeau
Abstrak
AbstractWe 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 $\mathbb{R}_{+}$.
Penulis (2)
Y
Yasser Farhat
F
Frédéric Gourdeau
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2018
- Bahasa
- en
- Sumber Database
- CrossRef
- DOI
- 10.4153/s0008439518000644
- Akses
- Open Access ✓