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Doctoral Thesis
DOI
10.11606/T.55.2006.tde-23022007-144550
Document
Author
Full name
Luciene Nogueira Bertoncello
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2006
Supervisor
Committee
Levcovitz, Daniel (President)
Bergamasco, Adalberto Panobianco
Coutinho, Severino Collier
Hernandes, Marcelo Escudeiro
Ripoll, Cydara Cavedon
Title in Portuguese
Algumas conjecturas sobre ideais principais maximais de álgebras de Weyl
Keywords in Portuguese
Álgebra não comutativa
Álgebras de Weyl
Derivações simples
Abstract in Portuguese
Seja d:= '\partial'/'\partial IND.x'+ 'beta\partial'/'partial IND.y'uma derivação simples de K[x,y], onde K é um corpo de característica zero. Doering, Lequain e Ripoll ([1]) provaram que exite um 'gama''PERTENCE A' K[x,y] tal que o operador S = '\partial'/'\partial x'+'beta\partial'/'\partial y'+'gama''PERTENCE A''A IND.2'':= K[x,y]' < '\partial'/partial IND.x', '\partial'/'partial'/'partial IND y''>'gera um ideal à esquerda maximal principal de 'A IND.2'. Desta maneira mostraram, para n=2, que a seguinte conjectura é verdadeira: Seja d:='\partial'/ '\partial IND.x"IND.1"+"alfa'IND.2''\partial'/'\partial'IND.x''IND.2"+...+ alfa IND.n"\partial'/'\partial IND.x''IND.n" uma derivaçào simples de K['x IND.1'...'x IND n']. Então, A IND.n'(d+'gama') é um ideal à esquerda maximal principal de Á IND.n', para algum 'gama''PERTENCE A'K['x IND.1',...'x IND.n']. Nós mostramos que esta conjectura é verdadeira em alguns casos particulares
Title in English
Some conjectures about principal maximal ideals of the Weyl álgebra
Keywords in English
Noncommutative álgebra
Simple derivations
Weyl álgebras
Abstract in English
Let d: ='\partial/'/'\partial IND.x'+ 'beta\partial IND.y' be a simple derivation of K[x,y], where K is a field of characteristic zero. Doering, Lequain e Ripol ([1]) proved that there exists a polynomial um 'gama''IT BELONGS' K[x,y] such that the operador S ='\partial'/'\partial x'+'beta\partial'/'\partial y''gama''IT BELONGS'' á ind.2':= K[x,y]' < '\partial'/'partial IND.x','partial'/'partial'/'partial IND y'> 'generates a principal maximal left ideal of A IND.2'. In this way, they showed that, for n=2, the following conjectures is tru: Let d:='\partial'/'\partial IND.x"+"alfaÍND.2"\partial'/ "\partial' IND.x'IND.2"+ álfa IND.n"\partial IND.xÍND.n"be a simple derivation of K['x IND.1',...,'x IND n']. Then, 'A IND.n'(d+'gama') is a principal maximal left ideal of 'A IND.n',for some 'gama"IT BELONGS'K[x IND.1',...,'x IND.n']. We show that this conjecture is true in some cases
 
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Publishing Date
2007-02-26
 
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