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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.1999.tde-20210729-023023
Document
Author
Full name
Rosana Retsos Signorelli Vargas
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1999
Supervisor
Title in Portuguese
Álgebras de tipo mesh fortemente simplesmente conexas
Keywords in Portuguese
Anéis E Álgebras Não Associativos
Abstract in Portuguese
O objetivo deste trabalho é estudar a seguinte classe de álgebras. Seja 'delta' uma aljava finita, com translação e 'capa' um corpo algebricamente fechado. A álgebra dada pelo quociente de 'capa'delta' pelo ideal gerado por suas relações de tipo mesh é chamada de álgebra de tipo mesh de 'delta. Tal classe de álgebras inclui as álgebras hereditárias e as de Auslander. Tendo em mente as álgebras de Auslander, iremos estudar aqui as álgebras de tipo mesh do ponto de vista de suas propriedades homológicas, assim como seu tipo de representação, extensões por um ponto, existência de componentes pós-projetivas. Como resultado principal obtivemos uma caracterização das álgebras de tipo mesh que são fortemente simplesmente conexas em termos da cohomologia de Hochschild, condição de separação, contornos irredutíveis e grafos-órbitas
Title in English
not available
Abstract in English
The purpose of this work is to study the following class of algebras. Let 'delta' be a finite translation quiver and 'capa' be an algebraically closed field. The algebra given by the quotient of 'capa'delta' by the ideal generated by its mesh relations is called the mesh algebra of 'delta'. Such a class of algebras include the hereditary and the Auslander algebras. Having in mind the Auslander algebras, we shall study here the mesh algebras concerning their homological properties, as well as its representation type, one-point extensions, existence of postprojective components. As a main result, we shall obtain a characterization of mesh algebras which are strongly connected in terms of the Hochschild cohomology, the separation condition, irreducible contours and orbit-graphs
 
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Publishing Date
2021-07-29
 
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