| 李雅南,高寿兰,刘 东.李代数$W(2,2)$上的Poisson结构[J].数学年刊A辑,2016,37(3):267~272 |
| 李代数$W(2,2)$上的Poisson结构 |
| Poisson Structure on the Lie Algebra $W(2,2)$ |
| Received:February 06, 2015 Revised:September 10, 2015 |
| DOI： |
| 中文关键词: 李代数W(2,2), Poisson代数, Leibniz 法则, Virasoro 代数 |
| 英文关键词: |
| 基金项目:本文受到国家自然科学基金 (No.11371134, No.11201141)
和浙江省自然科学基金项目(No.LZ14A010001, No.LQ12A01005, No.LY16A010016)的资助. |
| Author Name | Affiliation | | LI Yanan | Department of Mathematics, Huzhou University,
Huzhou 313000, Zhejiang, China. | | GAO Shoulan | Department of Mathematics, Huzhou University,
Huzhou 313000, Zhejiang, China. | | LIU Dong | Corresponding author. Department of Mathematics, Huzhou University,
Huzhou 313000, Zhejiang, China. |
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| 中文摘要: |
| Poisson代数是指同时具有代数结构和李代数结构的一类代数,
其乘法和李代数乘法满足Leibniz法则.
李代数$W(2,2)$在权为2的向量生成的顶点算子代数的分类中起着重要作用.
文章主要确定了李代数$W(2,2)$上的Poisson结构, 并得到了Virasoro代数上一般的非结合的Poisson结构,
改进了文[姚裕丰. Witt代数和Virasoro代数上的Poisson代数结构 [J]. {\kaishu 数学年刊}, 2013, 34A(1):111--128]
的部分结果. |
| 英文摘要: |
| Poisson algebras are algebras with an algebra structure and a Lie
algebra structure, both of which satisfy the Leibniz law. The Lie
algebra $W(2,2)$ plays a key role in classification of vertex
operator algebras generated by weight $2$ vectors. The authors mainly
determine the Poisson structure on $W(2,2)$ and the Poisson
structure on the Virasoro algebra, which partially improve results in
[Yao Y F. Poisson algebra structures on the Witt algebra and the
Virasoro algebras [J]. {\it Chinese Ann Math}, 2013, 34A(1):111--128]. |
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