Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations

• 来源期刊: 代数集刊（英文版）
• 关键词: multiparameter quantized Weyl algebras algebra automorphisms isomorphism problem quantum Dixmier conjecture
• 年，卷（期）: 2017,（3）
• 页码范围: 419-438
• 页数: 20页
• 语种: 英文
• DOI: 10.1142/S100538671700027X

摘要

We study a family of "symmetric" multiparameter quantized Weyl algebras A(q)∧n(K) and some related algebras.We compute the Nakayama automorphism of A(q),∧n(K),give a necessary and sufficient condition for A(q),∧n(K) to be Calabi-Yau,and prove that A(q),∧n(K) is cancellative.We study the automorphisms and isomorphism problem for A(q),∧n(K) and A(q),∧n(K[t]).Similar results are established for the Maltsiniotis multiparameter quantized Weyl algebra A(q),Γ(K) and its polynomial extension.We prove a quantum analogue of the Dixmier conjecture for a simple localization (A(q),∧n(K))Z and determine its automorphism group.