Realization of Poisson enveloping algebra

Can ZHU, Yaxiu WANG

Front. Math. China ›› 2018, Vol. 13 ›› Issue (4) : 999-1011.

PDF(179 KB)
PDF(179 KB)
Front. Math. China ›› 2018, Vol. 13 ›› Issue (4) : 999-1011. DOI: 10.1007/s11464-018-0708-x
RESEARCH ARTICLE
RESEARCH ARTICLE

Realization of Poisson enveloping algebra

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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.

Keywords

Poisson enveloping algebra / quantized universal enveloping algebra / deformation quantization

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Can ZHU, Yaxiu WANG. Realization of Poisson enveloping algebra. Front. Math. China, 2018, 13(4): 999‒1011 https://doi.org/10.1007/s11464-018-0708-x

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