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Semiclassical Limits of Ore Extensions and a Poisson Generalized Weyl Algebra

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Abstract

We observe [Launois and Lecoutre, Trans. Am. Math. Soc. 368:755–785, 2016, Proposition 4.1] 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, a necessary and sufficient condition is obtained, 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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  1. Department of Mathematics, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon, 34134, Korea

    Eun-Hee Cho & Sei-Qwon Oh

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  1. Eun-Hee Cho
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  2. Sei-Qwon Oh
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Correspondence to Sei-Qwon Oh.

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Cho, EH., Oh, SQ. Semiclassical Limits of Ore Extensions and a Poisson Generalized Weyl Algebra. Lett Math Phys 106, 997–1009 (2016). https://doi.org/10.1007/s11005-016-0856-4

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  • DOI: https://doi.org/10.1007/s11005-016-0856-4

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