(Quasi-)Poisson enveloping algebras

• DOI: 10.1007/s10114-012-1041-z
• Publication Date: 2012-09-22T07:16:44Z
• Authors: Yan Hong Yang; Yuan Yao; Yu Ye
• Keywords: Poisson algebra

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.<br/>17 pages<br/>