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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.1998.tde-20210729-020856
Document
Author
Full name
Cecilia Tosar Escuder
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1998
Supervisor
Title in Portuguese
Representações de álgebras de Artin projetivamente estáveis
Keywords in Portuguese
Álgebra
Anéis E Álgebras Associativos
Abstract in Portuguese
Este trabalho está baseado nos artigos [JK1], [JK2] e [JK3] escritos por Jagadeeshan e Kleiner. Nosso objetivo é estudar uma classe de álgebras de Artin, a saber as álgebras projetivamente estáveis, e descrever as categorias de módulos finitamente gerados sobre elas. Para tanto analisamos a estrutra de tais álgebras e descrevemos o quiver de Auslander-Reiten correspondente. Tal classe de álgebras surge naturalmente tendo em vista a noção de categoria projetivamente estável e a definição do funtor Tr (transposta). Quanto à estrutura, provamos que uma semisimples. Como consequência desse resultado vemos que obtemos o quiver de Auslander-Reiten de uma álgebra hereditária e de certa álgebra serial. Por último, como aporte pessoal ao trabalho, comparamos as álgebras estudadas com outras classes de álgebras de Artin: as quase -inclinadas, as shod e as ' P IND.1'-hereditárias
Title in English
not available
Abstract in English
This work is based on the papers [JK1], [JK2] and [JK3] written by Jagadeeshan and Kleiner. Our main aim is to introduce a class of Artin algebras, the projectively stable algebras, and to describe the categories of finitely generated modules over them. For this, we analize the structure of such algebras and we describe their Auslander-Reiten quivers. That class of algebras appears naturaly taking into account the notion of projectively stable category and the definition of the functor Tr (transpose). With regard to the structure, we show that such an algebra is either serial, or the pullback of a hereditary algebra and a serial algebra over a semisimple algebra. As a consequence of this result it is shown that one can obtain the Auslander-Reiten quiver of a projectively stable algebra from the Auslander-Reiten quiver of a hereditary algebra and of certain serial algebra. Finally, as a personal contribution to the work, we compare the studied algebras with other classes of Artin algebras: the quasetilted, the shod and 'P IND.1'-hereditary
 
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Publishing Date
2021-07-29
 
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