Two-parameter analogs of the Heisenberg enveloping algebra
arXiv:1308.4427 · doi:10.1080/00927872.2015.1101468
Abstract
One-parameter analogs of the Heisenberg enveloping algebra were studied previously by Kirkman and Small. In particular, they demonstrated how one may obtain Hayashi's analog of the Weyl algebra as a primitive factor of this algebra. We consider various two-parameter versions of this problem. Of particular interest is the case when the parameters are dependent. Our study allows us to consider the representation theory of a two-parameter version of the Virasoro enveloping algebra.
Sections 3,4, and 5 have now been merged into Section 3 of the current manuscript. References added. The various cases corresponding to relations between the parameters are now divided into Sections 4, 5, and 6