(Quasi-)Poisson enveloping algebras

Authors
Yang, Yan Hong Yao, Yuan Ye, Yu
Citation
Yang, Yan Hong et al., (Quasi-)Poisson enveloping algebras, Acta mathematica Sinica. English series (Print) , 29(1), 2013, pp. 105-118
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
29
Issue
1
Year of publication
2013
Pages
105 - 118
Database
ACNP
SICI code
Abstract
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.