Heisenberg代数的导子和型心的矩阵表示  

The matrix representations of derivations and centroids of the Heisenberg algebra

作　　者：杨茹惠 郑克礼[1,2] YANG Ruhui;ZHENG Keli(Department of Mathematics,College of Science,Northeast Forestry University,Harbin 150040,China;Institute of Cold Regions Science and Engineering,Northeast Forestry University,Harbin 150040,China)

机构地区：[1]东北林业大学理学院数学系,哈尔滨黑龙江150040 [2]东北林业大学工程咨询设计研究院有限公司,哈尔滨黑龙江150040

出　　处：《纯粹数学与应用数学》2025年第1期169-178,共10页Pure and Applied Mathematics

基　　金：中央高校基本科研业务费专项资金项目资助(2572021BC02);黑龙江省博士后资助经费(LBH-Z23068);黑龙江省高等教育教学改革项目(SJGY20220130).

摘　　要：本研究旨在计算Heisenberg代数的导子和型心的矩阵表示.通过定义导子和型心,并运用解线性方程组的方法,确定了2n+1维Heisenberg代数的导子矩阵和型心矩阵.研究结果表明,2n+1维Heisenberg代数的导子与一个分块矩阵同构(定理3.1),而其型心的矩阵表示为一个对角阵加上边矩阵(定理3.2).这些计算结果为Heisenberg代数的深入研究提供了具体的理论基础.The purpose of this study is to calculate the matrix representations of the derivations and centroids of the Heisenberg algebra.By de ning derivations and centroids,and using methods to solve systems of linear equations,we have determined the derivation matrices and center matrices for the(2n+1)-dimensional Heisenberg algebra.The results show that the derivations of the(2n+1)-dimensional Heisenberg algebra are isomorphic to a block matrix(Theorem 3.1),and the matrix representation of the centroid of the(2n+1)-dimensional Heisenberg algebra is a diagonal matrix with additional side matrices(Theorem 3.2).These calculations provide a concrete theoretical foundation for further research on the Heisenberg algebra.

关 键 词：HEISENBERG代数 导子 型心 矩阵表示 

分 类 号：O152.5[理学—数学]