(Quasi-)Poisson enveloping algebras
Rings and Algebras
2010-12-14 v2 Category Theory
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.
Cite
@article{arxiv.1011.5411,
title = {(Quasi-)Poisson enveloping algebras},
author = {Yan-Hong Yang and Yuan Yao and Yu Ye},
journal= {arXiv preprint arXiv:1011.5411},
year = {2010}
}
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17 pages