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Doctoral Thesis
DOI
Document
Author
Full name
Oscar Daniel Lopez Osorio
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Guzzo Junior, Henrique (President)
Araujo, Wilian Francisco de
Fernandez, Juan Carlos Gutierrez
Gorshkov, Ilya
Lopatin, Artem
Title in Portuguese
Nova álgebra de Lie simples de dimensão 30 sobre um corpo de característica 2
Keywords in Portuguese
Algebras simples
Base toroidal absoluta
Posto toroidal
Abstract in Portuguese
S.Skryabin demonstrou que qualquer álgebra de Lie simples de dimensão finita sobre um corpo de característica 2 possui posto toroidal 2. Duas 2- álgebras de Lie de dimensão 31 foram estudadas. Neste trabalho, mostramos que a primeira delas contem uma base toroidal absoluta de dimensão três, assim como a segunda, que foi estudada por Grishkov e Guerreiro anteriormente. Utilizando uma decomposicão de Cartan, exibimos um isomorfismo entre as duas 2- álgebras de Lie de dimensão 31. Este resultado foi sugerido depois de encontrar uma sub álgebra de dimensão 12 n ao solúvel e 7 isomorfas 2-sub álgebras de Lie de dimensão 7 nas duas álgebras. Finalmente, exploramos uma 2- álgebra de Lie de dimensão 34 como o fim de encontrar base toroidal absoluta de dimensão 4. Apoiamos os cálculos com algumas códigos no linguajem de MATLAB que permitiram optimizar e acelerar a pesquisa.
Title in English
A new 30 dimensional simple lie algebra on a field of characteristic 2
Keywords in English
Absolute toral rank
Maximal toral subalgebra
Simples algebras
Abstract in English
S.Skryabin showed that any finite dimensional simple Lie algebra over a field of characteristic 2 has absolute toral rank 2. Two 31-dimensional 2-algebras were known. In this work, we show that the first of these algebras, contains a 3-dimensional maximal toral subalgebra, as the second one, which was studied by Grishkov e Guerreiro previously. Using a Cartan decomposition we establish an isomorphism between the two 31-dimensional 2-algebras. This result was suggested after finding a 12-dimensional not soluble subalgebra and seven 7-dimensional isomorphic 2-subalgebras in both algebras. Finally, a 34-dimensional 2-Lie algebra was studied in order to find 4-dimensional maximal toral subalgebras. Some computations in this work were performed with help of MATLAB.
 
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Publishing Date
2019-04-30
 
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