Abstract
For a Poisson algebra, the category of Poisson modules is equivalent to the module category of its Poisson enveloping algebra, where the Poisson enveloping algebra is an associative one. In this article, for a Poisson structure on a polynomial algebra S, we first construct a Poisson algebra R, then prove that the Poisson enveloping algebra of S is isomorphic to the specialization of the quantized universal enveloping algebra of R, and therefore, is a deformation quantization of R.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant No. 11771085).
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Zhu, C., Wang, Y. Realization of Poisson enveloping algebra. Front. Math. China 13, 999–1011 (2018). https://doi.org/10.1007/s11464-018-0708-x
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DOI: https://doi.org/10.1007/s11464-018-0708-x