Universal enveloping algebras of Poisson Ore extensions
Universal enveloping algebras of Poisson Ore extensions
复制标题
DOI：
10.1090/s0002-9939-2015-12631-7
复制
发表时间：
2014-03
期刊：
影响因子：
--
通讯作者：
Jia-Feng Lu;Xingting Wang;G. Zhuang
中科院分区：
文献类型：
--
作者：
Jia-Feng Lu;Xingting Wang;G. Zhuang
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.
