Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra

Eun-Hee Cho; Sei-Qwon Oh

doi:10.1007/s11005-016-0856-4

paper

Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra

arXiv:1602.02195 · doi:10.1007/s11005-016-0856-4

Abstract

We observe \cite[Proposition 4.1]{LaLe} that Poisson polynomial extensions appear as semiclassical limits of a class of Ore extensions. As an application, a Poisson generalized Weyl algebra $A_{1}$ considered as a Poisson version of the quantum generalized Weyl algebra is constructed and its Poisson structures are studied. In particular, it is obtained a necessary and sufficient condition such that $A_{1}$ is Poisson simple and established that the Poisson endomorphisms of $A_{1}$ are Poisson analogues of the endomorphisms of the quantum generalized Weyl algebra.

10 pages