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Doctoral Thesis
DOI
10.11606/T.45.2012.tde-05022015-111007
Document
Author
Full name
Paula Andrea Cadavid Salazar
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Marcos, Eduardo do Nascimento (President)
Alvares, Edson Ribeiro
Bekkert, Viktor
Martins, Maria Izabel Ramalho
Mernies, Marcelo Americo Lanzilotta
Title in Portuguese
Sistemas estratificantes sobre álgebras hereditárias
Keywords in Portuguese
Álgebras hereditárias
Módulos inclinantes
Sequências excepcionais
Sistemas estratificantes
Abstract in Portuguese
O principal tema deste trabalho é o estudo dos sistemas estratificantes sobre álgebras hereditárias. Um dos principais problemas é a construção de sistemas estratificantes completos cujos elementos sejam todos módulos regulares, sendo este problema resolvido para álgebras hereditárias do tipo mansa e as álgebras de Kronecker generalizadas. Para as álgebras hereditárias de tipo mansa exibimos um limitante para o tamanho dos sistemas estratificantes formados só de módulos regulares e, usando tal limitante, concluímos que não é possível que tais sistemas estratificantes sejam completos. Para as álgebras de Kronecker e as álgebras de Kronecker generalizadas concluimos que nenhum sistema estratificante sobre esta álgebra pode ter elementos regulares e construímos todos os possíveis sistemas estratificantes completos sobre esta álgebra. Definimos o conceito de sequência especial de um módulo inclinante, estabelecemos que todo módulo inclinante tem uma sequência especial e estudamos quando uma sequência, de dois e três somandos diretos de um módulo inclinante, é uma sequência especial.
Title in English
Stratifying systems over hereditary algebras
Keywords in English
Exceptional sequences
Hereditary algebras
Stratifying systems
Tilting modules
Abstract in English
The main topic of this work is the study of stratifying systems over hereditary algebras. One of the main questions to be considered is the construction of complete stratifying systems whose elements are regular modules. We solve this problem for tame hereditary algebras and for the Kronecker generalized algebras. In the case of tame hereditary algebras, we obtain a bound for the size of the stratifying systems composed only by regular modules and, by using this bound, we conclude that such stratifying systems can not be complete. For the Kronecker and for Kronecker the generalized algebras we conclude that no stratifing system over this algebra can have regular elements. Next we construct all possible complete stratifying systems over this algebra. Furthermore, we define the notion of special sequence of a tilting module and we establish that all tilting modules have an special ordenation. Also we study when an sequence of two and three direct summands of an tilting module, is a special ordenation.
 
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tese_Paula_Cadavid.pdf (822.27 Kbytes)
Publishing Date
2015-02-25
 
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