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Doctoral Thesis
DOI
10.11606/T.45.2019.tde-15022019-084657
Document
Author
Full name
Camilo Andres Angulo Santacruz
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Gonzalez, Cristian Andres Ortiz (President)
Brahic, Olivier
Bursztyn, Henrique
Cabrera, Alejandro
Struchiner, Ivan
Title in English
A cohomology theory for Lie 2-algebras and Lie 2-groups
Abstract in English
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and Lie groups in that their second groups classify extensions. We use this fact together with an adapted van Est map to prove the integrability of Lie 2-algebras anew.
Title in Portuguese
Uma teoria de cohomologia para 2-algebras de Lie e 2-grupos de Lie
Keywords in Portuguese
Cohomologia
Geometria de ordem superior
Teoria de Lie
Abstract in Portuguese
Nesta tese, nós introduzimos uma nova teoria de cohomologia associada às 2-álgebras de Lie e uma nova teoria de cohomologia associada aos 2-grupos de Lie. Prova-se que estas teorias de cohomologia estendem as teorias de cohomologia clássicas de álgebras de Lie e grupos de Lie em que os seus segundos grupos classificam extensões. Finalmente, usaremos estos fatos junto com um morfismo de van Est adaptado para encontrar uma nova prova da integrabilidade das 2-álgebras de Lie.
 
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Thesis.pdf (1.43 Mbytes)
Publishing Date
2019-03-26
 
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