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- Title
PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras.
- Authors
Hu, Xianguo; Lü, Jiafeng; Wang, Xingting
- 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.
- Subjects
POISSON algebras; UNIVERSAL algebra; DIFFERENTIAL algebra; COMMUTATIVE algebra; POLYNOMIAL rings; ALGEBRA; POISSON'S equation
- Publication
Bulletin of the Malaysian Mathematical Sciences Society, 2019, Vol 42, Issue 6, p3343
- ISSN
0126-6705
- Publication type
Article
- DOI
10.1007/s40840-018-0673-2