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arXiv · 1403.5852

Universal enveloping algebras of Poisson Ore extensions

Jiafeng Lü·Xingting Wang·Guangbin Zhuang
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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 consequences, 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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Jiafeng Lü, Xingting Wang, Guangbin Zhuang. 2014-03-24. Universal enveloping algebras of Poisson Ore extensions. https://doi.org/10.1090/s0002-9939-2015-12631-7

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