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Doctoral Thesis
DOI
10.11606/T.55.2017.tde-14112017-102821
Document
Author
Full name
Leandro Nery de Oliveira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Manoel, Miriam Garcia (President)
Antoneli Junior, Fernando Martins
Buzzi, Claudio Aguinaldo
Dias, Fábio Scalco
Ruas, Maria Aparecida Soares
Title in Portuguese
Aspectos da teoria invariante e equivariante para a ação do grupo de Lorentz no espaço de Minkowski
Keywords in Portuguese
Espaço de Minkowski
Grupo de Lorentz
Teoria equivariante
Teoria invariante
Abstract in Portuguese
Neste trabalho, introduzimos a teoria invariante e equivariante para a ação do grupo de Lorentz no espaço de Minkowski. Na teoria clássica, muitos resultados são válidos somente para a ação de grupos compactos em espaços Euclideanos. Continuamos o estudo para alguns subgrupos de Lorentz compactos e apresentamos uma forma de calcular as involuções de Lorentz em O(n;1). Fazemos uma empolgante discussão sobre uma classe de matrizes centrossimétricas polinomiais com aplicações em teoria invariante, estabelecendo um rumo para a pesquisa em subgrupos de Lorentz não compactos. Por fim, apresentamos alguns resultados da teoria equivariante para subgrupos de Lorentz.
Title in English
Aspects of the invariant and equivariant theory for the action of the Lorentz group in Minkowski space
Keywords in English
Equivariant theory
Invariant theory
Lorentz group
Minkowski space
Abstract in English
In this work, we introduce the invariant and equivariant theory for the Lorentz group on the Minkowski space. In the classical theory, many results are valid only for compact groups on Euclidean spaces. We continue the study of some compact Lorentz subgroups and present a way of calculating the Lorentz involutions in O(n;1). We make an exciting discussion about a class of polynomial centrosymmetric matrices with applications in invariant theory, setting a course for research in non-compact Lorentz groups. Finally, we present some results for the equivariant theory of Lorentz subgroups.
 
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Publishing Date
2017-11-14
 
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