Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

Abstract

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.