
Realization of Poisson enveloping algebra
Can ZHU, Yaxiu WANG
Front. Math. China ›› 2018, Vol. 13 ›› Issue (4) : 999-1011.
Realization of Poisson enveloping algebra
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.
Poisson enveloping algebra / quantized universal enveloping algebra / deformation quantization
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