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Doctoral Thesis
DOI
10.11606/T.45.2007.tde-21072007-114130
Document
Author
Full name
Anliy Natsuyo Nashimoto Sargeant
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Futorny, Vyacheslav (President)
Chestakov, Ivan
Guerreiro, Marinês
Kochloukov, Plamen Emilov
Moura, Adriano Adrega de
Title in Portuguese
Módulos tipo Verma sobre álgebra TKK afim estendida
Keywords in Portuguese
álgebra de Lie afim estendida
álgebra TKK afim estendida
módulo de Verma
Abstract in Portuguese
As álgebras TKK afins estendidas pertencem à classe de álgebras de Lie chamada álgebras de Lie afins estendidas do tipo $A_1$. Elas são obtidas a partir de um semi-reticulado do $\mathbbR^n$. Estudamos a estrutura dos módulos tipo Verma sobre a álgebra TKK afim estendida para um semi-reticulado (não-reticulado) do $\mathbbR^2$. Quando fixamos um conjunto positivo de raízes isotrópicas chamado standard encontramos quatro órbitas da subálgebra de Borel que dão origem a distintos módulos tipo Verma sobre a álgebra TKK afim estendida. Estudamos as estruturas de seus submódulos e encontramos critérios de irredutibilidade para os módulos de Verma clássico e imaginário.
Title in English
Verma type module over an extended affine TKK algebra.
Keywords in English
extended affine Lie algebra
extended affine TKK algebra
Verma module
Abstract in English
The extended affine TKK Lie algebras belong to a class of Lie algebras called extended affine Lie algebras of type $A_1$. They are obtained from a semilattice on $\mathbbR^n$. We studied the structure of the Verma type modules for the extended affine TKK algebra obtained from a semi-lattice (non-lattice) on $\mathbbR^2$. Fixing a set of positive isotropic roots called standard we found four orbits of the Borel subalgebra each of which give distinct Verma modules for the extended affine TKK algebra. We studied the structures of their submodules and found a criteria for irreducibility for the classic and imaginary Verma modules.
 
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Publishing Date
2009-01-28
 
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