Sweedler四维代数及其子代数上的带权无穷小双代数和预李代数  

Weighted Infinitesimal Bialgebras and Pre-Lie Algebras on the Sweedler 4-dimensional Algebra and Its Subalgebras

作　　者：曹靖涵 张凌佳 张毅 郑慧慧[2] CAO Jing-han;ZHANG Ling-jia;ZHANG Yi;ZHENG Hui-hui(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Mathematics and Statistics,Henan Normal University,Xinxiang 4530032,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044 [2]河南师范大学数学与统计学院,河南新乡453032

出　　处：《数学的实践与认识》2022年第9期201-212,共12页Mathematics in Practice and Theory

基　　金：国家自然科学基金(12101316);南京信息工程大学大学生创新训练项目(XJDC202110300406)。

摘　　要：带权无穷小双代数是非齐次结合经典杨巴方程的代数抽象,在数学和数学物理领域有诸多重要的应用.给出了Sweedler四维代数及其子代数上的带权无穷小双代数的分类.作为应用,得到了Sweedler四维代数上的预李代数,进而诱导出它们的李代数结构.The weighted infinitesimal bialgebra is an algebraic abstract of the nonhomogenous associative classical Yang-Baxter equation.It has many important applications in the fields of mathematics and mathematical physics.In this paper,we give a classification of weighted infinitesimal bialgebras on the Sweedler 4-dimensional algebra and its subalgebras.As applications,the pre-Lie algebras and induced Lie algebras on the Sweedler 4-dimensional algebra are also obtained.

关 键 词：无穷小双代数 Sweedler四维代数 预李代数 李代数 

分 类 号：O152.5[理学—数学]