多重线性多项式在3 × 3阶上三角矩阵代数上的像

孙爱慧; 白杰; 包开花

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

doi: 10.3969/j.issn.1000-5641.201911047

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

基金项目: 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)

详细信息

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

中图分类号: O153.3
计量
- 文章访问数: 74
- HTML全文浏览量: 76
- PDF下载量: 4
- 被引次数: 0
出版历程
- 收稿日期: 2019-12-09
- 刊出日期: 2021-01-27

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

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

摘要

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.
- 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.
- Lvov-Kaplansky conjecture /
- multilinear polynomial /
- upper triangular matrix algebra /
- triangular algebra

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参考文献(14)

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