Automorphisms for Some Symmetric Multiparameter Quantized Weyl Algebras and Their Localizations（Dedicated to Professor Yingbo Zhang on her 70th birthday）  

作　　者：Xin Tang Xin Tang(Department of Mathematics ＆ Computer Science Fayetteville State University, 1200 Murchison Road Fayetteville, NC 28301, USA)

机构地区：[1]Department of Mathematics & Computer Science Fayetteville State University, 1200 Murchison Road Fayetteville, NC 28301, USA

出　　处：《Algebra Colloquium》2017年第3期419-438,共20页代数集刊（英文版）

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

关 键 词：multiparameter quantized Weyl algebras algebra automorphisms isomor-phism problem quantum Dixmier conjecture 

分 类 号：O153[理学—数学] O152.1[理学—基础数学]