Prime ideals of quantized Weyl algebras

Abstract

The main object of study in this paper is the quantized Weyl algebra which arises from the work of Maltsiniotis [10] on noncommutative differential calculus. This algebra has been studied from the point of view of noncommutative ring theory by various authors including Alev and Dumas [1], the second author [9], Cauchon [3], and Goodearl and Lenagan [5]. In [9], it is shown that has n normal elements zi and, subject to a condition on the parameters, the localization obtained on inverting these elements is simple of Krull and global dimension n. It is easy to show that each of these normal elements generates a height one prime ideal and that these are all the height one prime ideals of . The purpose of this paper is to determine, under a stronger condition on the parameters, all the prime ideals of and to compare the prime spectrum with that of a related algebra . This algebra has more symmetric defining relations than those of but it shares the same simple localization which again is obtained by inverting n normal elements zi. Like the alternative algebra can be regarded as an algebra of skew differential (or difference) operators on the coordinate ring of quantum n-space.

Équivalence rationnelle d'algèbres polynomiales classiques et quantiques

“…Dans le cas où tous les λ i,j valent 1, l'algèbre S (1) n,r (k) est l'algèbre de Weyl A r (k[y r+1 , . .…”

“…, q n ) valent tous 1. En particulier, l'algèbre S Λ 2,2 (k) = A (1,1),Λ 2 (k) est déjà considérée dans [3] (voir aussi le début de la section 5 de cet article). Les algèbres S Λ n,n (k) sont simples, et de centre k (voir [17], et le chapitre 5 de [29]).…”

Prime and Primitive Ideals of a Class of Iterated Skew Polynomial Rings

“…Hence C n T = C n T + 1. Applying Remark 4.4 (1) to T , we get C n T = C n−1 T + 1. The second case is that n − i r − 1 is odd, so C n T = C n−2 T + 1 C n T = C n−2 T + 1 and thus, C n T = C n T = C n−1 T + 1 by Remark 4.4(1) applied to T .…”

Sur une classe d'extensions de Ore itérées

“…, ν n ,ν n ) ∈ N 2n , alors On note par R l'algèbre R (C,Λ) n (k). Considérons l'ordre lexicographique ≺ lex avec y 1 ≺ lex x 1 ≺ lex · · · ≺ lex y n ≺ lex x n sur l'ensemble des monômes de R, X ν = y ν 1 1 xν 1 1 · · · y ν n n xν n n | ν = (ν 1 ,ν 1 , . .…”

“…Brown et K.R. Goodearl [3], effectuées par M. Akhavizadegan dans [1]. La description des cliques des idéaux premiers dans R (C,Λ) n (k) nous permettra d'étudier les ensembles et les idéaux (classiquement) localisables, en utilisant des résultats classiques de [16,18,30].…”