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Master's Dissertation
DOI
Document
Author
Full name
Maria Clara Cardoso
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Futorny, Vyacheslav (President)
Calixto, Lucas Henrique
Kochloukov, Plamen Emilov
Title in Portuguese
Subálgebras de Mischenko-Fomenko de álgebras envolventes de álgebras de Lie simples
Keywords in Portuguese
Problema de Vinberg
Subálgebra de Mishchenko-Fomenko
Variedade de Gelfand-Tsetlin
Abstract in Portuguese
Nesse trabalho introduzimos as subálgebras de Mishchenko-Fomenko. Apresentamos o problema de Vinberg e a solução de Feigin, Frenkel e Toledano-Laredo em Feigin, Frenkel e Toledano-Laredo (2010) Também é mostrada a solução para as álgebras de Lie de tipo A apresentada em Futorny e Molev (2015). É estudado também o artigo Molev (2013) onde são apresentados geradores do centro de Feigin-Frenkel para as álgebras de Lie de tipo B, C e D. Também são introduzidas as subálgebras de Gelfand-Tsetlin, subálgebras das álgebras envolventes universais das álgebras de Lie de tipo A. Apresentamos uma definição de súbálgebra de Gelfand-Tsetlin para as álgebras de Lie de tipo C, introduzida em Molev e Yakimova (2017). São exibidas as variedades de Gelfand-Tsetlin de $\mathfrak_$ e $\mathfrak_$, sendo provado que a variedade de Gelfand-Tsetlin de $\mathfrak_$ é equidimensional de dimensão 4. Também é demonstrado um novo resultado sobre a equidimensionalidade de $\mathfrak_$.
Title in English
Mishchenko-Fomenko subalgebras of universal enveloping algebras of simple Lie algebras
Keywords in English
Gelfand-Tsetlin variety
Mishchenko-Fomenko subalgebras
Vinberg's problem
Abstract in English
In this dissertation, we introduce the Mishchenko-Fomenko subalgebras. We show Vinberg's problem and the solution given by Feigin, Frenkel and Toledano-Laredo in Feigin, Frenkel and Toledano-Laredo (2010). We also show a solution for Lie algebras of type A found in Futorny and Molev (2015). We study the article Molev (2013) where generators for the Feigin-Frenkel center are shown for Lie algebras of type B, C and D. We introduce the Gelfand-Tsetlin subalgebras, which are subalgebras of the universal enveloping algebras of Lie algebras of type A. We show a definition of Gelfand-Tsetlin for Lie algebras of type C, introduced in Molev and Yakimova (2017). We exhibit the Gelfand-Tsetlin varieties related to $\mathfrak_$ and $\mathfrak_$. We prove that the Gelfand-Tsetlin variety for $\mathfrak_$ is equidimensional of dimension 4 and we prove a new result about the equidimensionality of $\mathfrak_$.
 
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Publishing Date
2019-09-12
 
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