Universal Central Extension of Two Classes of Trigonometric Lie Algebras

Abstract

李代数$\mathcal{A}$是复数域$\mathbb{C}$上的$A_{h}$型三角函数李代数,$\mathcal{A}$的一组基为$\{A_{m,n}|m,n\in\mathbb{Z}\setminus\{(0,0)\}\}$,且满足下面的李运算: [A_{m_{1},n_{1}},A_{m_{2},n_{2}}]=2isin(h(m_{2}n_{1}-m_{1}n_{2}))A_{m_{1}+m_{2},n_{1}+n_{2}}. 李代数$\mathfrak{B}$是$\mathbb{C}$上的$B_{h}$型三角函数李代数,$\mathfrak{B}$由$\{B_{m,n}|m,...Let$\mathcal{A}$be a trigonometric Lie algebra of type$A_{h}$over$\mathbb{C}$with basis$\{A_{m,n} |m,n\in\mathbb{Z}\setminus \{(0,0)\}\}$and relations: [A_{m_{1},n_{1}},A_{m_{2},n_{2}}]=2isin(h(m_{2}n_{1}-m_{1}n_{2}))A_{m_{1}+m_{2},n_{1}+n_{2}}. Let$\mathfrak{B}$be a trigonometric Lie algebra of type$B_{h}$over$\mathbb{C}$,$\mathfrak{B}$is generated by$\{B_{m,n} |m,n\in\mathbb{...学位：理学硕士院系专业：数学科学学院数学与应用数学系_基础数学学号：1902011115251