Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra

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.

arXiv comment10 pages

References in corpus (3)

• Automorphisms of the Weyl algebra
• Poisson brackets and Poisson spectra in polynomial algebras
• Endomorphisms of quantum generalized Weyl algebras

Cited by in corpus (2)

• The generalized Weyl Poisson algebras and their Poisson simplicity criterion
• Automorphism groups of deformations and quantizations of Kleinian singularities