Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations
Abstract
We study a family of "symmetric" multiparameter quantized Weyl algebras Anq,λ(K) and some related algebras. We compute the Nakayama automorphism of Anq,λ(K), give a necessary and sufficient condition for Anq,λ(K) to be Calabi-Yau, and prove that Anq,λ(K) is cancellative. We study the automorphisms and isomorphism problem for Anq,λ(K) and Anq,λ(K[t]). Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra AnΓ(K) and its polynomial extension. We prove a quantum analogue of the Dixmier conjecture for a simple localization (Anq,λ(K))Z and determine its automorphism group.
This paper has been withdrawn.