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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.2021.tde-02062021-102157
Document
Author
Full name
Sidney Henrique Dale Cróde
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2021
Supervisor
Committee
Chestakov, Ivan (President)
Futorny, Vyacheslav
Kochloukov, Plamen Emilov
Mello, Thiago Castilho de
Petrogradsky, Victor
Title in Portuguese
Álgebras de Jordan de tipo hermitiano e de Weyl e derivações localmente nilpotentes de álgebra livre associativa
Keywords in Portuguese
Automorfismos mansos
Derivações localmente nilpotentes
Dimensão de Gelfand-Kirillov
Primeira álgebra de Weyl
Abstract in Portuguese
Na primeira parte deste trabalho, estudamos a dimensão de Gelfand-Kirillov de álgebras simétricas H(A,*) e de álgebras associativas com involução (A,*). Além disso, damos uma contribuição relacionando as dimensões de Gelfand-Kirillov de H(A,*) e (A,*). Na segunda parte, provamos que o conjunto dos elementos simétricos de uma álgebra alternativa com involução é finitamente gerado, que é análogo ao teorema de Osborn para álgebras associativas. Além disso, consideramos duas álgebras de Jordan relacionadas a primeira álgebra de Weyl A_1 e encontramos suas representações em termos de geradores e relações. Por fim, estudamos derivações localmente nilpotentes da álgebra livre associativa K< x,y> (K corpo de característica zero) e mostramos que elas são triangularizáveis. Como aplicação, damos uma nova prova de que os automorfismos de K< x,y> são mansos.
Title in English
Jordan algebra of hermitian type, Jordan Weyl algebra and locally nilpotent derivations free associative algebra
Keywords in English
First Weyl algebra
Gelfand-Kirillov dimension
Locally nilpotent derivations
Tame automorphisms
Abstract in English
In the first part of this work, we study the Gelfand-Kirillov dimension of symmetric algebras H(A,*) and associative algebras with involution (A,*). In addition, we make a contribution by relating the Gelfand-Kirillov dimensions of H(A,*) and (A,*). In the second part, we prove that the set of symmetric elements of an alternative algebra with involution is finitely generated, which is analogous to Osborn's theorem for associative algebras. In addition, we consider two Jordan algebras related with the first Weyl algebra A_1 and find their representations in terms of generators and relations. Finally, we study locally nilpotent derivations of free associative algebra K< x,y> (K field of characteristic zero) and show that they are triangularizable. As an application, we give new proof that the automorphisms K< x,y> are tame.
 
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tese_IME_USP.pdf (664.86 Kbytes)
Publishing Date
2021-07-06
 
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