特殊线性群SL(2,R)的有限Abelian子群  

Special Linear Group SL(2,R) of Finite Abelian Subgroup

作　　者：蒋传华 段翠连 

机构地区：[1]广西师范大学,广西桂林

出　　处：《应用数学进展》2017年第4期627-636,共10页Advances in Applied Mathematics

摘　　要：本文运用λ-矩阵的相关理论和常系数线性齐次递归关系的求解方法,对特殊线性群SL(2,R) 的有限Abelian子群进行了研究,给出了其任意阶循环群的结构,即2阶矩阵方程: 且 ,其中 的全部解。进一步,我们希望通过探讨各阶循环群生成元的交换性来确定 SL(2,R) 的有限Abelian子群结构。In this paper, we study the finite Abelian subgroup of special linear group SL(2,R) by using the eigenvalue theory of λ-matrix and the solution method of constant coefficient linear homogeneous recursive relations. We get the structure of cyclic group for arbitrary order n of SL(2,R) , that is to say, all the solutions of the 2 order matrix equation: and ( ) are given out. Furthermore, we hope to determine the structure of finite Abelian subgroup of special linear group SL(2,R) by discussing the commutativity between generators of arbitrary order cyclic group.

关 键 词：特殊线性群 Abelian群 齐次递归关系 Λ-矩阵 

分 类 号：O1[理学—数学]