一类无限维李代数上的李双代数结构

发布时间：2018-06-04 18:45

本文选题：Yang-Baxter方程 + 仿射Schr?dinger　；参考：《黑龙江大学》2015年硕士论文

【摘要】：在数学和物理学的许多分支中,以单变量的Laurent多项式环为坐标代数的仿射Kac-Moody代数及其表示都有着非常重要的应用.而仿射Schr¨odinger Lie代数作为Laurent多项式代数重要推广,已经得到了很多学者的研究.本文研究了仿射Schr¨odinger Lie代数上的双代数结构.Lie双代数是既具有Lie代数结构又具有Lie余代数结构的向量空间.本文的第一章主要介绍了Lie双代数的国内外发展现状、趋势以及本文的研究目的和意义.第二章,我们首先回顾了Lie双代数的概念及一些基础知识,并介绍了所研究的仿射Schr¨odinger Lie代数和一些相关导子的结论.第三章,证明了本文的主要结果,仿射Schr¨odinger Lie代数上的Lie双代数结构是三角上边缘的.
[Abstract]:In many branches of mathematics and physics, affine Kac-Moody algebras with univariate Laurent polynomial rings as coordinate algebras and their representations have very important applications. As an important generalization of Laurent polynomial algebra, affine Schr odinger Lie algebra has been studied by many scholars. In this paper, we study the bialgebraic structure on affine Schr odinger Lie algebras. Lie bialgebras are vector spaces with both Lie algebraic structures and Lie coalgebraic structures. The first chapter of this paper mainly introduces the development of Lie bialgebra at home and abroad, the trend and the purpose and significance of this paper. In chapter 2, we first review the concept and some basic knowledge of Lie bialgebra, and introduce the results of affine Schr algebra and some related derivations. In chapter 3, we prove that the structure of Lie bialgebras on affine Schr odinger Lie algebras is triangular-edge.
【学位授予单位】：黑龙江大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O152.5

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