(Quasi-)Poisson enveloping algebras

Details (Quasi-)Poisson enveloping algebras (Quasi-)Poisson enveloping algebras

2010-11-24

arxiv.org/abs/1011.5411v2

Mathematics

Rings and Algebras

17 pages

Scientific paper

We introduce the quasi-Poisson enveloping algebra and Poisson enveloping algebra for a non-commutative Poisson algebra. We prove that for a non-commutative Poisson algebra, the category of quasi-Poisson modules is equivalent to the category of left modules over its quasi-Poisson enveloping algebra, and the category of Poisson modules is equivalent to the category of left modules over its Poisson enveloping algebra.

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