The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 an...The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 and G\-2, the inductions of complete prime Abel orbit datum are independent of the Choice of parabolic subgroups.展开更多
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The purpose of the present note is to prove that the parabolic inductions of the orbit datum and Dixmier algebras can be induced by stages. And as an appliction, we have proved that for SO(2n+1, C), SP(2n, C), F\-4 and G\-2, the inductions of complete prime Abel orbit datum are independent of the Choice of parabolic subgroups.
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.
