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(Quasi-)Poisson enveloping algebras

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arxiv 1011.5411 v2 pith:Q7H6CMPY submitted 2010-11-24 math.RA math.CT

(Quasi-)Poisson enveloping algebras

Yan-Hong Yang , Yuan Yao , Yu Ye This is my paper
classification math.RA math.CT
keywords algebrapoissonenvelopingcategorymodulesquasi-poissonequivalentleft
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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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