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...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.展开更多
文摘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.