PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras
PBW-Basis for Universal Enveloping Algebras of Differential Graded Poisson Algebras
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DOI：
10.1007/s40840-018-0673-2
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发表时间：
2018-09
影响因子：
1.2
通讯作者：
Xianguo Hu;Jia-feng Lü;Xingting Wang
中科院分区：
文献类型：
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作者：
Xianguo Hu;Jia-feng Lü;Xingting Wang
对由生成元和关系给定的微分分次Poisson代数A，给出了计算其泛包络代数的“公式”。证明了当A是分次交换多项式代数时，A是Poincaré-Birkhoff-Witt基.作为PBW-基的应用，我们证明了DG Poisson代数A的DG辛理想是单DG Poisson A-模的零化子，其中A是DG Poisson代数R的DG Poisson同态像，R的代数结构是分次交换多项式代数.
For any differential graded (DG for short) Poisson algebraAgiven by generators and relations, we give a “formula” for computing the universal enveloping algebraofA. Moreover, we prove thathas a Poincaré–Birkhoff–Witt basis provided thatAis a graded commutative polynomial algebra. As an application of the PBW-basis, we show that a DG symplectic ideal of a DG Poisson algebraAis the annihilator of a simple DG PoissonA-module, whereAis the DG Poisson homomorphic image of a DG Poisson algebraRwhose underlying algebra structure is a graded commutative polynomial algebra.