《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
乔宁,房莹,张良云*
QIAO Ning, FANG Ying, ZHANG Liang-yun*
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。
中图分类号:
[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. |
|