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arXiv · 1602.02195

Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra

Eun-Hee Cho·Sei-Qwon Oh
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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.

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Eun-Hee Cho, Sei-Qwon Oh. 2016-02-23. Semiclassical limits of Ore extensions and a Poisson generalized Weyl algebra. https://doi.org/10.1007/s11005-016-0856-4

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