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Master's Dissertation
DOI
10.11606/D.45.2007.tde-12122014-121334
Document
Author
Full name
Paula Andrea Cadavid Salazar
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2007
Supervisor
Committee
Marcos, Eduardo do Nascimento (President)
Martins, Maria Izabel Ramalho
Mernies, Marcelo Americo Lanzilotta
Title in Portuguese
Álgebras estandarmente estratificadas e álgebras quase-hereditárias
Keywords in Portuguese
álgebras estandarmente estratificadas
álgebras quase-hereditárias
módulos estandares
Abstract in Portuguese
Sejam K um corpo algebricamente fechado, A uma K-álgebra básica conexa de dimensão finita sobre K e ê=(e_1,e_2,... ,e_n) um conjunto completo de idempotentes ortogonais, primitivos e ordenados de A. O conjunto dos módulos estandares é o conjunto Delta ={ D_1, ..., D_n }, onde D_i é o quociente maximal do A-módulo projetivo P_i com fatores de composição simples S_j, com j\leq i, F(Delta) é a subcategoria plena de mod A dos módulos têm uma Delta-filtração. Se A_A esta em F(Delta) diz-se que A é uma álgebra estandarmente estratificada. Se, além disso, para cada elemento em Delta vale que End_A(D_i) é isomorfo a K diz-se que A é uma álgebra álgebra quase-hereditária. Nesta dissertação estudamos as propriedades de F(Delta), especialmente quando A é estandarmente estratificada, e algumas condições necessárias e suficientes para que A seja quase-hereditária.
Title in English
Standardly stratified algebras and quasi-hereditary algebras
Keywords in English
quasi-hereditary algebras
standard modules
standardly stratified algebras
Abstract in English
Let K be an algebraically closed field, A a basic, connected, finite dimensional K-algebra and ê=(e_1,e_2,...,e_n) a complete set of ordered primitive orthogonal idempotents of A. The set of standard modules is the set Delta={D_1, ..., D_n}, where D_i is the maximal factor submodule of P_i whose composition factors are isomorphic to S_j, for j\leq i. We denote by F(Delta) the full subcategory of mod A containing the modules which are filtered by modules in Delta. If iA_A is in F(Delta) we say that A is standardly stratified. Moreover, if End_A(D_i) is isomorphic with K, for each element in Delta we say that A is quasi hereditary. In this work we study the properties of the category F(Delta), especially when A is stardardly stratified, and some necessary and sufficient conditions to A be quasi hereditary.
 
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Publishing Date
2015-01-05
 
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