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Realization of Poisson enveloping algebra |
Can ZHU( ), Yaxiu WANG |
| College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China |
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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.
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| Keywords
Poisson enveloping algebra
quantized universal enveloping algebra
deformation quantization
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Corresponding Author(s):
Can ZHU
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Issue Date: 14 August 2018
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