Existence of extensions of semilattices of groups by groups, cohomology, and crossed modules for inverse semigroups
We introduce the concept of a partial abstract kernel associated to a pair (G, A), where G is a group and A is a semilattice of groups, and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kerne...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | Brasil |
| Institución: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-16062020-172746 |
| Acceso en línea: | https://www.teses.usp.br/teses/disponiveis/45/45131/tde-16062020-172746/ |
| Access Level: | acceso abierto |
| Palabra clave: | Abstract kernel Ação parcial Cohomologia de ação parcial Cohomologia de semigrupos inversos Extensions Extensões Inverse semigroup cohomology Inverse semigroups Núcleo abstrato Partial action Partial group cohomology Semigrupos inversos Semilattices of groups Semirreticulados de grupos |
| Sumario: | We introduce the concept of a partial abstract kernel associated to a pair (G, A), where G is a group and A is a semilattice of groups, and relate the partial cohomology group H^3(G,C(A)) with the obstructions to the existence of admissible extensions of A by G which realize the given abstract kernel. Also, if such extensions exist, we show that they are classified by H^2(G,C(A)). We define the notion of a crossed module over inverse semigroups and construct a corresponding 4-term sequence. To each equivalence class of such sequences we relate an element of the third order-preserving inverse semigroup cohomology, so that we have a bijection in the case of a semilattice of groups. |
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