本文選題：Yang-Baxter方程 + 仿射Schr?dinger　； 參考：《黑龍江大學(xué)》2015年碩士論文

【摘要】：在數(shù)學(xué)和物理學(xué)的許多分支中,以單變量的Laurent多項(xiàng)式環(huán)為坐標(biāo)代數(shù)的仿射Kac-Moody代數(shù)及其表示都有著非常重要的應(yīng)用.而仿射Schr¨odinger Lie代數(shù)作為Laurent多項(xiàng)式代數(shù)重要推廣,已經(jīng)得到了很多學(xué)者的研究.本文研究了仿射Schr¨odinger Lie代數(shù)上的雙代數(shù)結(jié)構(gòu).Lie雙代數(shù)是既具有Lie代數(shù)結(jié)構(gòu)又具有Lie余代數(shù)結(jié)構(gòu)的向量空間.本文的第一章主要介紹了Lie雙代數(shù)的國內(nèi)外發(fā)展現(xiàn)狀、趨勢以及本文的研究目的和意義.第二章,我們首先回顧了Lie雙代數(shù)的概念及一些基礎(chǔ)知識,并介紹了所研究的仿射Schr¨odinger Lie代數(shù)和一些相關(guān)導(dǎo)子的結(jié)論.第三章,證明了本文的主要結(jié)果,仿射Schr¨odinger Lie代數(shù)上的Lie雙代數(shù)結(jié)構(gòu)是三角上邊緣的.
[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.
【學(xué)位授予單位】：黑龍江大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：O152.5

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本文編號：1978460