Poisson流形上李代数与Poisson辛李群的讨论

Lie Algebra on The Poisson Manifold and Poisson Symplectic Lie Group

文章给出了Poisson流形上李括号的一些结论,并在Poisson流形P1,P2上定义了C∞(P1)C∞(P2)的{,}运算,验证了C∞(P1)C∞(P2)构成李代数,其次简单讨论了Poisson辛李群。

In the paper,we give some conclusions about Lie bracket on the Poisson manifold . and defined {, }operation of C^∞ （P1）＋C^∞（P2） on Poisson manifolds of P1,P2, at the same time,we test and verified that C^∞（P1）＋C^∞（P2） forms Lie algebra,and then we discuss Poisson symplectic Lie group.