Algumas conjecturas sobre ideais principais maximais de álgebras de Weyl / Some conjectures about principal maximal ideals of the Weyl álgebra

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

Let d: =\partial//\partial IND.x+ beta\partial IND.ybe 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 gamaIT BELONGSK[x,y] such that the operador S =\partial/\partial x+beta\partial/\partial ygamaIT BELONGSá 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/ "\partialIND.xIND.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 BELONGSK[x IND.1,...,x IND.n]. We show that this conjecture is true in some cases

ASSUNTO(S)

Álgebra não comutativa weyl álgebras noncommutative álgebra simple derivations Álgebras de weyl derivações simples

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