# PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras

@article{Hu2014PBWBasisFU, title={PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras}, author={Xianguo Hu and Jiafeng L{\"u} and Xingting Wang}, journal={Bulletin of the Malaysian Mathematical Sciences Society}, year={2014}, pages={1-35} }

For any differential graded (DG for short) Poisson algebra A given by generators and relations, we give a “formula” for computing the universal enveloping algebra $$A^e$$Ae of A. Moreover, we prove that $$A^e$$Ae has a Poincaré–Birkhoff–Witt basis provided that A is a graded commutative polynomial algebra. As an application of the PBW-basis, we show that a DG symplectic ideal of a DG Poisson algebra A is the annihilator of a simple DG Poisson A-module, where A is the DG Poisson homomorphic… CONTINUE READING

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