Algumas conjecturas sobre ideais principais maximais de álgebras de Weyl

Bertoncello, Luciene Nogueira

doi:10.11606/T.55.2006.tde-23022007-144550

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DOI

https://doi.org/10.11606/T.55.2006.tde-23022007-144550

Document

Doctoral Thesis

Author

Bertoncello, Luciene Nogueira (Catálogo USP)

Full name

Luciene Nogueira Bertoncello

Institute/School/College

Instituto de Ciências Matemáticas e de Computação

Knowledge Area

Mathematics

Date of Defense

2006-07-07

Published

São Carlos, 2006

Supervisor

Levcovitz, Daniel (Catálogo USP)

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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