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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-31032017-141121
Document
Author
Full name
Carlos Rafael Payares Guevara
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
As 2-álgebras de Lie simples de posto toral 3
Keywords in Portuguese
2-álgebras de Lie
Posto toral
Simples
Abstract in Portuguese
Neste trabalho estudamos as 2-álgebras de Lie simples, de dimensão finita e de posto toral 3, sobre um corpo algebricamente fechado de característica 2. Nós conjecturamos que a única 2-álgebra de Lie simples de este tipo é W(1, 3). Assim, nosso principal objetivo é verificar a veracidade desta conjectura para estas álgebras de pequenas dimensões. Como resultados, provamos que esta conjectura é certa para todas estes álgebras de dimensão menor ou igual a 16, e também em alguns casos especiais quando a dimensão é 17.
Title in English
Simple Lie 2-algebras of toral rank 3
Keywords in English
Lie 2-algebras
Simple
Toral rank
Abstract in English
In this work we study the simple Lie 2-algebras of finite dimension, and toral rank 3 over an algebraically closed field characteristic 2. We surmise that the only simple Lie 2-algebra of this type is W(1, 3). So, our main objective is to study the truthful of this conjecture for these algebras of small dimensions. As a result, we prove that this conjecture is true for all these algebras less than or equal to 16 dimension, and also in some special cases when the dimension is 17.
 
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Publishing Date
2017-04-03
 
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