若当块不大于七阶的十一阶矩阵群幂单性  

The Unipotency of Eleventh Order Matrix Group with no More than Seven Jordan Blocks

作　　者：杨新松 高云峰 YANG Xinsong;GAO Yunfeng(School of Science,Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2024年第2期137-146,共10页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

摘　　要：针对二元生成矩阵群的幂单性问题,避开了抽象的李代数,李超代数等理论的研究方法,采用矩阵对数、非交换多项式乘积的展开等简单理论,讨论并发现了新的二元生成自由群本原元组合性质。基于这些新的二元生成自由群本原元的组合性质,首次就一般矩阵群给出了组合性质的统一证明并得到新的关于矩阵迹的方程,在此基础上首次利用流程图归纳了此类证明的流程,并借助计算软件maple,求解所得的方程,再利用相似变换得到了新的幂单性质的判定条件,丰富了相关研究。By avoiding complex research methods involving Lie algebra and Lie superalgebra,and instead utilizing simple theories such as matrix logarithm and expansion of product of non commutative polynomial,the new combination property of primitive elements of binary generated free groups is explored intensively against the problem of unipotent of binary generated matrix groups.A unified proof of the combination property is given for the general matrix group initiatively using the primitive elements of the binary generated free group with a new equation for the matrix trace obtained.Based on this,a flowchart is primarily used to summarize the proofing process.At the same time,the equation is solved by maple,the calculation software,before the new judgment condition of the unipotency is obtained from the similarity transformation.This approach enriches the content of related research.

关 键 词：本原元 矩阵群 幂单性 自由群 

分 类 号：O153.3[理学—数学]