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Master's Dissertation
DOI
10.11606/D.45.2016.tde-12092016-205141
Document
Author
Full name
André Silva de Oliveira
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2016
Supervisor
Committee
Futorny, Vyacheslav (President)
Bekkert, Viktor
Iusenko, Kostiantyn
Title in Portuguese
Classificação de módulos de peso sobre álgebras de Weyl
Keywords in Portuguese
Álgebras de Weyl
Módulos de peso indecomponíveis
Módulos de peso simples
Abstract in Portuguese
Neste trabalho, introduzimos as álgebras de Weyl clássicas A = A_n e as generalizadas A = D(sigma, a). Apresentamos algumas propriedades importantes dessas álgebras, dentre outras, que a n-ésima álgebra de Weyl A_n é um domínio simples Noetheriano à esquerda. Introduzimos os módulos de peso sobre A e estudamos os A-módulos de peso projetivos. Iniciamos a classificação dos A-módulos de peso simples (isto é, irredutíveis) através de uma categoria linear C_O e do seu esqueleto S_O cf. A classificação total dos A_infty-módulos de peso simples é dada utilizando a ação de certas localizações no anel de polinômios cf. Classificamos os blocos do tipo mansa na categoria dos A-módulos de peso localmente finitos e determinamos os A-módulos indecomponíveis nos blocos do tipo mansa. Seguindo, descrevemos os A-módulos de peso injetivos e projetivos indecomponíveis e deduzimos uma descrição dos blocos na categoria dos A-módulos de peso por quivers e relações.
Title in English
Classification of weight modules over Weyl algebras
Keywords in English
Indecomposable weight modules
Simple weight modules
Weyl algebras
Abstract in English
In this dissertation, we introduce the classical Weyl algebras A = A_n and the generalized A = D(sigma, a). There are some important properties of these algebras, among others, that the n-th Weyl algebra A_n is a left Noetherian simple domain. We introduced the weight modules over A and study the projective weight A-modules. Started the classification of simple weight A-modules (this is, irreducible) by linear category C_O and its skeleton S_O in accordance with. The complete classification of simple weight A-modules is given using the action of certain localizations in the polynomial ring in accordance with. We classify the tame blocks in the category of locally-finite weight A-modules and determine the indecomposable A-modules in the tame blocks. Following, we describe indecomposable projective and injective weight A-modules and deduce the description of the blocks in the category of weight A-modules by quivers and relations.
 
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Publishing Date
2016-09-20
 
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