[en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS

• Main Author: MARTIN PABLO SANTACATTERINA
• Other Authors: NICOLAU CORCAO SALDANHA
• Language: pt
• Published: MAXWELL 2017
• Subjects: [pt] ALGEBRA DE LIE; [en] LIE ALGEBRA; [pt] SUBALGEBRA DE CARTAN; [en] CARTAN SUBALGEBRA; [pt] SISTEMA DE RAIZES; [en] ROOT SYSTEM; [pt] DIAGRAMA DE DYNKIN; [en] DYNKIN DIAGRAM; [pt] DIAGRAMA DE SATAKE; [en] SATAKE DIAGRAM; [pt] GRUPO DE WEYL; [en] WEYL GROUP; [pt] FORMA REAL COMPACTA; [en] COMPACT REAL FORM; [pt] DECOMPOSICAO DE CARTAN; [en] CARTAN DECOMPOSITION; [pt] ABELIANO MAXIMAL; [en] MAXIMAL ABELIAN
• Online Access: https://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456@1; https://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=32456@2; http://doi.org/10.17771/PUCRio.acad.32456

[pt] Iniciamos o trabalho com uma revisão da classificação de álgebras de Lie semi-simples sobre corposo algebraicamente fechados de caracteristica zero a traves dos Diagramas de Dyinkin. Posteriormente estudamos sigma - sistemas normais e classificamos eles a traves de diagramas de Satake. Finalmente estudamos a estrutura das formas reais de álgebras de Lie semi-simples complexas, explicitando a conexão com os diagramas de Satake e fornecenendo assim uma classificação das mesmas. === [en] We begin the work with a review of the classification of semisimple Lie algebras over an algebraically field of characteristic zero through the Dyinkin Diagrams. Subsequently we study sigma - normal systems and classify them through Satake diagrams. Finally we study the structure of the real forms of complex semi-simple Lie algebras, explaining the connection with the Satake diagrams and thus providing a classification of them.