Frontiers of Mathematics in China >
Realization of Poisson enveloping algebra
Received date: 27 Jan 2018
Accepted date: 28 May 2018
Published date: 14 Aug 2018
Copyright
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.
Can ZHU , Yaxiu WANG . Realization of Poisson enveloping algebra[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 999 -1011 . DOI: 10.1007/s11464-018-0708-x
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