Universal enveloping algebras of Poisson Ore extensions

Lü, Jiafeng; Wang, Xingting; Zhuang, Guangbin

doi:10.1090/S0002-9939-2015-12631-7

Universal enveloping algebras of Poisson Ore extensions
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by Jiafeng Lü, Xingting Wang and Guangbin Zhuang PDF

Proc. Amer. Math. Soc. 143 (2015), 4633-4645 Request permission

Abstract:

We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As a consequence, we observe certain ring-theoretic invariants of the universal enveloping algebras that are preserved under iterated Poisson-Ore extensions. We apply our results to iterated quadratic Poisson algebras arising from semiclassical limits of quantized coordinate rings and a family of graded Poisson algebras of Poisson structures of rank at most two.

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