Universal enveloping algebras of Poisson Hopf algebras
Universal enveloping algebras of Poisson Hopf algebras
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DOI：
10.1016/j.jalgebra.2014.12.010
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发表时间：
2014-02
期刊：
影响因子：
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通讯作者：
Jia-Feng Lu;Xingting Wang;G. Zhuang
中科院分区：
文献类型：
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作者：
Jia-Feng Lu;Xingting Wang;G. Zhuang
对于泊松代数a，通过探索其与Lie-Rinehart代数的关系，证明了其普适包膜代数a e的poincar<s:1> - birkhoff - witt定理。研究了泊松霍普夫代数的普适包膜代数的一些一般性质。给定泊松Hopf代数B，给出了泊松多项式代数B [x]的充分必要条件；α， δ] p是泊松霍普夫代数。我们还证明了B是点泊松霍普夫代数时be的一个结构定理。即，be同构于b# σ H (B)，即B与H (B)的叉积，其中H (B)是商Hopf代数be / beb +。
For a Poisson algebra A, by exploring its relation with Lie–Rinehart algebras, we prove a Poincaré–Birkhoff–Witt theorem for its universal enveloping algebra A e. Some general properties of the universal enveloping algebras of Poisson Hopf algebras are studied. Given a Poisson Hopf algebra B, we give the necessary and sufficient conditions for a Poisson polynomial algebra B [x; α, δ] p to be a Poisson Hopf algebra. We also prove a structure theorem for B e when B is a pointed Poisson Hopf algebra. Namely, B e is isomorphic to B# σ H (B), the crossed product of B and H (B), where H (B) is the quotient Hopf algebra B e/B e B+.