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Doctoral Thesis
DOI
https://doi.org/10.11606/T.45.1998.tde-20210729-021208
Document
Author
Full name
Alegria Gladys Chalom
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 1998
Supervisor
Title in Portuguese
Extensões por um ponto de álgebras inclinadas mansas
Keywords in Portuguese
Álgebra
Abstract in Portuguese
Sabemos por [P1] que, dada uma álgebra 'lâmbda'mansa, teremos que a forma quadrática de Tits 'q IND.'lâmbda' é fracamente não negativa, isto é, se 'lâmbda é mansa então 'q IND.'lâmbda'(z)'>OU='0, para todo z vetor-dimensão de coordenadas positivas. Além disso, a recíproca foi provada para algumas famílias de álgebras, porém não é válida em geral. O propósito deste trabalho é provar que, para certas categorias vectorespaciais selvagens IK = Hom(M,B - mod), onde B é uma álgebra inclinada mansa e M é um módulo indecomponível, teremos a forma 'q IND.B[M]' fortemente indefinida, o que nos fornece recíprocas parciais do teorema acima
Title in English
not available
Abstract in English
We know, after [P1], that, given a tame algebra 'lâmbda', the Tits form 'q IND.'lâmbda' is weakly non negative. That is, if 'lâmbda' is tame then 'q IND.'lâmbda'(z)'>OU='0, for any dimension-vector z of positive coordinates. Moreover, the converse has been shown for some families of algebras, but it is not true in general. The purpose of this work is to show that for certain wild vectorspace categories IK = Hom(M, B - mod), where B is tame tilted and M is an indecomposable B-module we have 'q IND.B[M]' strongly indefinite. This will give parcial converses of the above theorem
 
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Publishing Date
2021-07-29
 
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