Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

We study a family of “symmetric” multiparameter quantized Weyl algebras [Formula: see text] and some related algebras. We compute the Nakayama automorphism of [Formula: see text], give a necessary and sufficient condition for [Formula: see text] to be Calabi-Yau, and prove that [Formula: see text] is cancellative. We study the automorphisms and isomorphism problem for [Formula: see text] and [Formula: see text]. Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra [Formula: see text] and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization [Formula: see text] and determine its automorphism group.

Representations of the Quantized Weyl Algebra Associated to the Quantum Plane

In this paper, some new modules over the rank two quantized Weyl algebra are presented. The isomorphism classes among these modules are also determined.