| Texto completo | |
| Autor(es): |
Alves, Marcelo Muniz
;
Dokuchaev, Mikhailo
;
Kochloukova, Dessislava H.
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | QUARTERLY JOURNAL OF MATHEMATICS; v. 75, n. 2, p. 49-pg., 2024-05-02. |
| Resumo | |
We study partial homology and cohomology from the ring theoretic point of view via the partial group algebra $\hspace{2pt} \mathbb{K}_{par} G$. In particular, we link the partial homology and cohomology of a group G with coefficients in an irreducible (resp. indecomposable) $\hspace{2pt} \mathbb{K}_{par} G$-module M with the ordinary homology and cohomology groups of a subgroup H of $G,$ where H depends on $M,$ with coefficients in an appropriate irreducible (resp. indecomposable) $\hspace{2pt} \mathbb{K} H$-module. Furthermore, we compare the standard cohomological dimension $cd_{\hspace{2pt} \mathbb{K}}(G)$ (over a field $\hspace{2pt} \mathbb{K}$) with the partial cohomological dimension $cd_{\hspace{2pt} \mathbb{K}}<^>{par}(G)$ (over $\hspace{2pt} \mathbb{K}$) and show that $cd_{\hspace{2pt} \mathbb{K}}<^>{par}(G) \geq cd_{\hspace{2pt} \mathbb{K}}(G)$ and that there is equality for $G = \mathbb{Z}$. (AU) | |
| Processo FAPESP: | 20/16594-0 - Anéis não comutativos e aplicações |
| Beneficiário: | Francisco Cesar Polcino Milies |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |
| Processo FAPESP: | 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos |
| Beneficiário: | Ivan Chestakov |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |