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Master's Dissertation
DOI
10.11606/D.45.2012.tde-13102012-133216
Document
Author
Full name
Silvana Kameyama
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2012
Supervisor
Committee
Marcos, Eduardo do Nascimento (President)
Fernandes, Sônia Maria
Lanzilotta, Marcelo
Title in Portuguese
Complexidade de Módulos
Keywords in Portuguese
álgebras autoinjetivas
Álgebras de Artin
carcás de Auslander-Reiten
complexidade
números Betti
resoluções projetivas
sequências de Auslander-Reiten.
Abstract in Portuguese
A complexidade de um módulo M, sobre uma álgebra de dimensão finita R, é a medida do crescimento da dimensão de suas sizigias. No nosso trabalho, estudamos esse conceito, nos concentrando muito mais no caso das álgebras autoinjetiva. Relacionamos esse crescimento com o comportamento da componente do carcás de Auslander-Reiten, a qual o módulo M pertence. Em particular, estudamos, com bastante cuidado, o caso em que a complexidade é 1, o que significa que a dimensão das sizigias são eventualmente constante. Surpreendentemente, o comportamento de todos os módulos numa mesma componente é muito parecido.
Title in English
Complexity of Modules
Keywords in English
Artin algebras
Auslander-Reiten quiver
Auslander-Reiten sequences.
Betti numbers
complexity
projectives resolutions
selfinjective algebras
Abstract in English
The complexity of a module M under a finite dimensional algebra R is the measure of the growth of its syzygies' dimension. In our work, we study this concept concentrating on the case of the selfinjective algebras. We relate this growth with the behavior of the Auslander-Reiten component containing this module. In particular, we study, carefully, the case in which the complexity is 1. Surprisingly, the behavior of every module in the same component as M is very similar.
 
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SilvanaKameyama.pdf (417.32 Kbytes)
Publishing Date
2012-10-18
 
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