您的位置:山东大学 -> 科技期刊社 -> 《山东大学学报(理学版)》

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (12): 56-62.doi: 10.6040/j.issn.1671-9352.0.2020.064

• • 上一篇    

Sweedler四维Hopf代数上的Poisson代数结构

乔宁,房莹,张良云*   

  1. 南京农业大学理学院, 江苏 南京 210095
  • 发布日期:2020-12-01
  • 作者简介:乔宁(1994— ), 女, 硕士研究生, 研究方向为Hopf代数. E-mail:307497159@qq.com*通信作者简介:张良云(1964— ), 男, 博士, 教授, 博士生导师, 研究方向为Hopf代数. E-mail:zlyun@njau.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11571173)

Structure of Poisson algebras on Sweedler 4-dimensional Hopf algebras

QIAO Ning, FANG Ying, ZHANG Liang-yun*   

  1. College of Science, Nanjing Agricultural University, Nanjing 210095, Jiangsu, China
  • Published:2020-12-01

摘要: 建立L-树状代数(L-dendriform algebra)、Rota-Baxter系统和Poisson代数之间的关系,将Poisson代数理论应用于Sweedler四维Hopf代数上构造Poisson代数和Poisson Hopf代数,对Rota-Baxter代数和Hopf代数的研究及应用有一定意义。

关键词: Poisson代数, Sweedler四维Hopf代数, L-树状代数, Rota-Baxter系统

Abstract: Constructing the relations among L-dendriform algebras, Rota-Baxter systems and Poisson algebras, and applying the theory of Poisson algebras to construct Poisson algebras and Poisson Hopf algebras on Sweedler 4-dimensional Hopf algebra are of significance to the research and application of Rota-Baxter algebras and Hopf algebras.

Key words: Poisson algebra, Sweedler 4-dimensional Hopf algebra, L-dendriform algebra, Rota-Baxter system

中图分类号: 

  • O153.3
[1] GOZE M, REMM E. Poisson algebras in terms of non-associative algebras[J]. Journal of Algebra, 2008, 320(1):294-317.
[2] AGUIAR M. Pre-Poisson algebras[J]. Letters in Mathematical Physics, 2000, 54(4):263-277.
[3] LÜ Jiafeng, WANG Xingting, ZHUANG Guangbin. Universal enveloping algebras of Poisson Hopf algebras[J]. Journal of Algebra, 2015, 426(1):92-136.
[4] LOU Qi, WU Quanshui. Co-Poisson structures on polynomial Hopf algebras[J]. Science China Mathematics, 2018, 61(5):813-830.
[5] SWEEDLER M E. Hopf algebras[M]. New York: Benjamin, 1969.
[6] BRZEZINSKI T. Rota-Baxter systems, dendriform algebras and covariant bialgebras[J]. Journal of Algebra, 2016, 460(1):1-25.
[7] AGUIAR M. Infinitesimal bialgebras, pre-Lie and dendriform algebras[J]. Lecture Notes in Pure and Applied Mathematics, 2004, 237(1):1-33.
[8] BAI Chengming, LIU Ligong, NI Xiang. Some results on L-dendriform algebras[J]. Journal of Geometry and Physics, 2010, 60(6):940-950.
[9] GUO Li. An introduction to Rota-Baxter algebra[M]. Beijing: Higher Education Press, 2012.
[10] 张倩, 李萱, 李歆, 等. 由Sweedler四维Hopf代数构造Rota-Baxter代数[J]. 山东大学学报(理学版), 2019, 54(6):47-52. ZHANG Qian, LI Xuan, LI Xin, et al. The construct of Rota-Baxter algebra on the Sweedler 4-dimensional Hopf algebra[J]. Journal of Shandong University(Natural Science), 2019, 54(6):47-52.
[1] 张倩,李萱,李歆,郑慧慧,李林涵,张良云. 由Sweedler四维Hopf代数构造Rota-Baxter代数[J]. 《山东大学学报(理学版)》, 2019, 54(6): 47-52.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
No Suggested Reading articles found!