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Master's Dissertation
DOI
https://doi.org/10.11606/D.55.2020.tde-19032020-093555
Document
Author
Full name
Pedro Henrique Carvalho Silva
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2020
Supervisor
Committee
Mencattini, Igor (President)
Cabrera, Alejandro
Ferreira, Carlos Henrique Grossi
Gonzalez, Cristian Andres Ortiz
Title in English
Central extensions and Symplectic Geometry
Keywords in English
Central extensions
Lie theory
Symplectic geometry
Abstract in English
This work explores aspects of Lie theory and its interactions with symplectic geometry. More precisely, we study a criterion to decide about the integrability of a given central extension of Lie algebras, which uses concepts from symplectic geometry in its formulation and finds an application in the context of hamiltonian actions. Futhermore, we discuss how some of the constructions appearing in the first part of this work may relate to the theory of Lie groupoids and Lie algebroids.
Title in Portuguese
Extensões Centrais e Geometria Simpléctica
Keywords in Portuguese
Extensões centrais
Geometria simpléctica
Teoria de Lie
Abstract in Portuguese
Este trabalho explora um pouco das interações da Teoria de Lie com a geometria simplética. Mais precisamente, estudamos um critério para a integrabilidade de extensões centrais de álgebras de Lie, o qual utiliza conceitos presentes também em geometria simplética e tem aplicação no contexto de ações hamiltonianas. Além disso, discutimos como algumas das estruturas aparecendo nesse primeiro contexto se relacionam com a teoria de groupóides e algebróides de Lie.
 
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Publishing Date
2020-03-19
 
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