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Showing 1 to 3 of 3 (0.043 seconds)Spelling suggestions: "subject:"[een] CARTAN SUBALGEBRA"" "subject:"[enn] CARTAN SUBALGEBRA""
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On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie AlgebrasGontcharov, Aleksandr 10 September 2013 (has links)
We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.
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On the Conjugacy of Maximal Toral Subalgebras of Certain Infinite-Dimensional Lie AlgebrasGontcharov, Aleksandr January 2013 (has links)
We will extend the conjugacy problem of maximal toral subalgebras for Lie algebras of the form $\g{g} \otimes_k R$ by considering $R=k[t,t^{-1}]$ and $R=k[t,t^{-1},(t-1)^{-1}]$, where $k$ is an algebraically closed field of characteristic zero and $\g{g}$ is a direct limit Lie algebra. In the process, we study properties of infinite matrices with entries in a B\'zout domain and we also look at how our conjugacy results extend to universal central extensions of the suitable direct limit Lie algebras.
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[en] CLASSIFICATION OF REAL SEMI-SIMPLE LIE ALGEBRAS BY MEANS OF SATAKE DIAGRAMS / [pt] CLASSIFICAÇÃO DE ÁLGEBRAS DE LIE SEMI-SIMPLES REAIS VIA DIAGRAMAS DE SATAKEMARTIN PABLO SANTACATTERINA 26 December 2017 (has links)
[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.
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