Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 37 (1996), No. 1, 119-148.

Spectre de l'alg\`ebre de Weyl quantique

Laurent Rigal

Abstract.

In this paper, we classify the prime spectrum of the quantized Weyl algebra
$A_{n}^{\bar{q},\Lambda}$
arising from the quantum differential calculus of G.\ Maltsiniotis
on the quantum multiparameter space.
$A_{n}^{\bar{q},\Lambda}$ is an algebra of differential operators on this space. It is shown that the set of non-maximal prime ideals is finite of
cardinality
${1\over 2}[(2 + \sqrt{2})^n+(2 - \sqrt{2})^n]$.
As a consequence, we prove that
$A_{n}^{\bar{q},\Lambda}$
is catenary. We also describe explicitly the automorphism group of this algebra.

MSC 1991: 16D30, 16P40, 17B37, 16S36, 16S32