多重线性多项式在3 × 3阶上三角矩阵代数上的像

doi:10.3969/j.issn.1000-5641.201911047

华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (1): 8-15.doi: 10.3969/j.issn.1000-5641.201911047

多重线性多项式在3 × 3阶上三角矩阵代数上的像

孙爱慧¹(), 白杰², 包开花³

1. 吉林师范大学数学学院, 吉林四平　136000
2. 上海师范大学数学系, 上海　200234
3. 内蒙古民族大学数理学院, 内蒙古通辽　028000

收稿日期:2019-12-09 出版日期:2021-01-25 发布日期:2021-01-28
作者简介:孙爱慧, 女, 博士, 副教授, 研究方向为代数学. E-mail: sunaihui2002@126.com
基金资助:
国家自然科学基金(11901322); 内蒙古自治区自然科学基金(2018LH01004); 吉林师范大学博士启动项目(吉师博2019001)

Images of multilinear polynomials on algebra of upper triangular 3 × 3 matrices

Aihui SUN¹(), Jie BAI², Kaihua BAO³

1. College of Mathematics, Jilin Normal University, Siping Jilin　136000, China
2. Department of Mathematics, Shanghai Normal University, Shanghai　200234, China
3. College of Mathematics and Physics, Inner Mongolia University for Nationalities, Tongliao Inner Mongolia　028000, China

Received:2019-12-09 Online:2021-01-25 Published:2021-01-28

摘要/Abstract

摘要：

借鉴Wang在研究 $ 2\times2$ 阶上三角矩阵代数上多重线性多项式的像时给出的新方法, 给出一个多重线性多项式在 $ 3\times3$ 阶上三角矩阵代数上像的结构的描述, 从而部分回答了Fagundes和Mello猜想, 此猜想是著名的Lvov-Kaplansky猜想的一种变化形式.

关键词: Lvov-Kaplansky猜想, 多重线性多项式, 上三角矩阵代数, 三角代数

Abstract:

This study builds on the method developed by Wang for images of multilinear polynomials on algebra of upper triangular $ 2\times2$ matrices. The main goal of the paper is to give a description of the images of multilinear polynomials on algebra of upper triangular $ 3\times 3$ matrices, thereby partly solving the Fagundes and Mello conjecture, a variation of the famous Lvov-Kaplansky conjecture.

Key words: Lvov-Kaplansky conjecture, multilinear polynomial, upper triangular matrix algebra, triangular algebra

中图分类号:

O153.3

孙爱慧, 白杰, 包开花. 多重线性多项式在3 × 3阶上三角矩阵代数上的像[J]. 华东师范大学学报（自然科学版）, 2021, 2021(1): 8-15.

Aihui SUN, Jie BAI, Kaihua BAO. Images of multilinear polynomials on algebra of upper triangular 3 × 3 matrices[J]. Journal of East China Normal University(Natural Science), 2021, 2021(1): 8-15.

参考文献 14

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多重线性多项式在3 × 3阶上三角矩阵代数上的像

Images of multilinear polynomials on algebra of upper triangular 3 × 3 matrices

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