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Master's Dissertation
DOI
10.11606/D.45.2017.tde-05122017-200848
Document
Author
Full name
Felipe Albino dos Santos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Futorny, Vyacheslav (President)
Bekkert, Viktor
Ramirez, Luis Enrique
Title in Portuguese
Módulos irredutíveis para subálgebras de Heisenberg de álgebras de Krichever-Novikov
Keywords in Portuguese
Álgebras de Heisenberg
Álgebras de Krichever-Novikov
Módulos phi-Verma
Abstract in Portuguese
Esta dissertação oferece uma introdução às já conhecidas álgebras de Krichever-Novikov se restringindo aos exemplos abordados previamente em Bremner (1995), Cox (2013), Cox e Jurisich (2013), Cox, Futorny e Martins (2014), Bueno, Cox e Furtony (2009), e as definições de estruturas que podem auxiliar a estudar estes espaços, incluindo álgebras de Lie afins, álgebras de loop e módulos de Verma. Considerando K uma álgebra de Krichever-Novikov do tipo 4-ponto, 3-ponto, elíptica ou DJKM e suas respectivas subálgebras de Heisenberg K' = K hK , onde hK é a subálgebra de Cartan de K , nos Teoremas 3.2.3, 3.4.3, 3.6.3 e 3.8.3 são apresentados critérios explícitos de irredutibilidade para K'-módulos do tipo -Verma.
Title in English
Representations of Heisenberg subalgebras of Krichever-Novikov algebras
Keywords in English
Heisenberg algebras
Krichever-Novikov algebras
Phi-Verma modules
Abstract in English
This work gives an introduction to the already known Krichever-Novikov algebras limited only to the examples approached before in Bremner (1995), Cox (2013), Cox e Jurisich (2013), Cox, Futorny and Martins (2014), Bueno, Cox and Furtony (2009), and the structures definitions that could help us to study these spaces, including affine Lie algebras, loop algebras and Verma modules. Let K be a 4-point, 3-point, elliptic or DJKM Krichever-Novikov algebra and its respective Heisenberg subalgebras K' = K hK , where hK is the K Cartan subalgebra. In the Theorems 3.2.3, 3.4.3, 3.6.3 and 3.8.3 we will give a explicit irreducibility criteria for -Verma K'-modules.
 
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Publishing Date
2017-12-07
 
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