PBW-basis for universal enveloping algebras of differential graded Poisson algebras

2017/04/05 by Hu, Xianguo, Lu, Jiafeng, Wang, Xingting · 1 citation
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1704.01319

Abstract

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 of A. Moreover, we prove that A^e 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 image of a DG Poisson algebra R whose underlying algebra structure is a graded commutative polynomial algebra.

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• Universal enveloping H-pseudoalgebras of DGP pseudoalgebras

Related

• Universal enveloping algebras of differential graded Poisson algebras
• The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras
• Poisson enveloping algebras and the Poincaré-Birkhoff-Witt theorem
• The PBW Theorem and simplicity criteria for the Poisson enveloping algebra and the algebra of Poisson differential operators
• Universal enveloping algebras of Poisson Hopf algebras