Universal enveloping algebras of Poisson Hopf algebras

作者：Lu, Jiafeng; Wang, Xingting; Zhuang, Guangbin^*

来源：Journal of Algebra, 2015, 426: 92-136.

DOI：10.1016/j.jalgebra.2014.12.010

• Hopf algebras
• Poisson Hopf algebras
• Universal enveloping algebras
• Lie-Rinehart algebras

For a Poisson algebra A, by exploring its relation with Lie-Rinehart algebras, we prove a Poincare-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; alpha, delta](p) to be a Poisson Hopf algebra. We also prove a structure theorem for B-e when B is a pointed Poisson Hopf algebra.

• 出版日期2015-3-15
• 单位浙江师范大学