Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
The present dissertation has as objective the study of the group A/Y ∼= S/S ∩ Y of outer automorphisms of the category of finitely generated free algebras for the variety of n-nilpotent linear algebras. There exists a conjecture that for every n we have A/Y ∼=k ∗o Autk. This conjecture was proved...
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| Formato: | Dissertação |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/33023 |
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| Resumo: | The present dissertation has as objective the study of the group A/Y ∼= S/S ∩ Y of
outer automorphisms of the category of finitely generated free algebras for the variety of
n-nilpotent linear algebras. There exists a conjecture that for every n we have A/Y ∼=k
∗o Autk. This conjecture was proved for n = 3, 4 and 5. We tried to prove this conjecture
for every n. The problem was not completely resolved, but some progress has been made.
The parameterization of the group S has been set. The associated decomposition of H, a
group which is very important for the calculation of the inner automorphisms, was proved.
One of the algorithms has been developed that can prove that H ≤ Y. After this, the
problem will be resolved. The complete solution of the problem under consideration could
be the subject of research for a doctoral dissertation. The study of the group A/Y for
every variety is very important in the area of Universal Algebraic Geometry, as far as this
group gives us the possible differences between geometric and automorphic equivalence of
algebras of the given variety. |
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