Doctoral Thesis
Document
Doctoral Thesis
Author
Full name
Luiz Felipe Villar Fushimi
Institute/School/College
Instituto de Matemática e Estatística
Knowledge Area
Date of Defense
2024-08-09
Published
São Paulo, 2024
Supervisor
Struchiner, Ivan
(
)
Committee
Struchiner, Ivan (President)
Cattafi, Francesco
Fernandes, Rui Loja
Gonzalez, Cristian Andres Ortiz
Pinzón, Maria Amelia Salazar
Title in English
Cartan structure groupoids and algebroids
Keywords in English
Cartan geometry, Lie algebroids, Poisson geometry
Abstract in English
This work concerns Cartan structure algebroids, a new synthesis of two other mathematical concepts: Cartan geometries and Lie algebroids. The objective of this synthesis is to provide a generalizing framework for the development of Lie theory of algebroids, most notably that of G-structure algebroids with connection. Aside from defining these objects and establishing their initial basic properties, we explore some developments of Lie theory of algebroids in which these algebroids may be used.
Title in Portuguese
Grupoides e algebroides de estrutura de Cartan
Keywords in Portuguese
Algebroides de Lie, Geometria de Cartan, Geometria de Poisson
Abstract in Portuguese
Este trabalho é sobre algebroides de estrutura de Cartan, uma nova síntese de dois outros conceitos matemáticos: geometrias de Cartan e algebroides de Lie. O objetivo desta síntese é providenciar um arcabouço generalizante para o desenvolvimento da teoria de Lie de algebroides, em particular a de algebroides de G-estrutura com conexão. Além de definir estes objetos e estabelecer suas propriedades iniciais básicas, exploramos alguns desenvolvimentos da teoria de Lie de algebroides nos quais estes algebroides podem ser utilizados.
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Publishing Date
2024-10-10
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