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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Autor principal: Teixeira, José Victor Gomes
Outros Autores: Tsurkov, Arkady
Formato: Dissertação
Idioma:pt_BR
Publicado em: Universidade Federal do Rio Grande do Norte
Assuntos:
Geometria algébrica universal
Teoria de categorias
Automorfismos fortemente estáveis
Álgebras lineares nilpotentes
Endereço do item:https://repositorio.ufrn.br/handle/123456789/33023
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spelling ri-123456789-330232021-08-27T17:44:13Z Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras Teixeira, José Victor Gomes Tsurkov, Arkady http://lattes.cnpq.br/9368785489596803 Kuzmin, Alexey Aladova, Elena Plotkin, Evgeny Geometria algébrica universal Teoria de categorias Automorfismos fortemente estáveis Álgebras lineares nilpotentes 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. Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES Essa dissertação tem como objetivo o estudo do grupo A/Y ∼= S/S ∩ Y dos automorfismos externos da categoria das álgebras livres finitamente geradas para a variedade das álgebras lineares n-nilpotentes. Há uma conjectura de que, para cada n, tem-se A/Y ∼=k∗ o Autk. Essa conjectura foi provada no caso em que n = 3, 4 e 5. Nós tentamos provar essa conjectura para todo n. O problema não foi completamente resolvido, mas foram feitos progressos. A parametrização do grupo S foi determinada, e a decomposição, associada a essa parametrização, de H, um grupo importante para o cálculo dos automorfismos internos, foi provada. Foi desenvolvido um dos algoritmos necessários para provar que H ≤ Y. Depois da demonstração dessa inclusão, o problema será resolvido. A resolução completa pode ser tópico de uma tese de doutorado. O estudo do grupo A/Y para cada variedade é muito importante na área de Geometria Algébrica Universal, pois ele informa sobre possíveis diferenças entre equivalência geométrica e equivalência automórfica de álgebras da variedade. 2021-08-05T17:36:51Z 2021-08-05T17:36:51Z 2021-07-05 masterThesis TEIXEIRA, José Victor Gomes. Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras. 2021. 81f. Dissertação (Mestrado em Matemática Aplicada e Estatística) - Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Natal, 2021. https://repositorio.ufrn.br/handle/123456789/33023 pt_BR Acesso Aberto application/pdf Universidade Federal do Rio Grande do Norte Brasil UFRN PROGRAMA DE PÓS-GRADUAÇÃO EM MATEMÁTICA APLICADA E ESTATÍSTICA
institution Repositório Institucional
collection RI - UFRN
language pt_BR
topic Geometria algébrica universal
Teoria de categorias
Automorfismos fortemente estáveis
Álgebras lineares nilpotentes
spellingShingle Geometria algébrica universal
Teoria de categorias
Automorfismos fortemente estáveis
Álgebras lineares nilpotentes
Teixeira, José Victor Gomes
Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
description 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.
author2 Tsurkov, Arkady
author_facet Tsurkov, Arkady
Teixeira, José Victor Gomes
format masterThesis
author Teixeira, José Victor Gomes
author_sort Teixeira, José Victor Gomes
title Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
title_short Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
title_full Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
title_fullStr Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
title_full_unstemmed Some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
title_sort some results on groups of outer automorphisms of categories of finitely generated nilpotent free algebras
publisher Universidade Federal do Rio Grande do Norte
publishDate 2021
url https://repositorio.ufrn.br/handle/123456789/33023
work_keys_str_mv AT teixeirajosevictorgomes someresultsongroupsofouterautomorphismsofcategoriesoffinitelygeneratednilpotentfreealgebras
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