数学

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
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  • 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
孙爱慧, 女, 博士, 副教授, 研究方向为代数学. E-mail: sunaihui2002@126.com

收稿日期: 2019-12-09

  网络出版日期: 2021-01-28

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 SUN ,
  • Jie BAI ,
  • Kaihua BAO
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  • 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 date: 2019-12-09

  Online published: 2021-01-28

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.

本文引用格式

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 . DOI: 10.3969/j.issn.1000-5641.201911047

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.

参考文献

1 KANEL-BELOV A, MALEV S, ROWEN L. Proc Amer Math Soc, The images of non-commutative polynomials evaluated on $ 2\times 2$ matrices . 2012, 140, 465- 478.
2 ANZIS B E, EMRICH Z M, VALIVETI K G. Linear Algebra Appl, On the images of Lie polynomials evaluated on Lie algebras. 2015, 469, 51- 75.
3 BUZINSKI D, WINSTANLEY R. Linear Algebra Appl, On multilinear polynomials in four variables evaluated on matrices. 2013, 439, 2712- 2719.
4 MESYAN Z. Linear and Multilinear A, Polynomials of small degree evaluated on matrices. 2013, 61, 1487- 1495.
5 KANEL-BELOV A, MALEV S, ROWEN L. Proc Amer Math Soc, The images of multilinear polynomials evaluated on $ 3\times 3$ matrices . 2016, 144, 7- 19.
6 ALBERT A, MUKENHOUPT B. Michigan Math J, On matrices of trace zero. 1957, 4, 1- 3.
7 KANEL-BELOV A, MALEV S, ROWEN L. J Pure Appl Algebra, Power-central polynomials on matrices. 2016, 220, 2164- 2176.
8 KANEL-BELOV A, MALEV S, ROWEN L. Comm Algebra, The images of Lie polynomials evaluated on matrices. 2017, 45, 4801- 4808.
9 MA A, OLIVA J. Linear Algebra Appl, On the images of Jordan polynomials evaluated over symmetric matrices. 2016, 492, 13- 25.
10 FAGUNDES P S. Linear Algebra Appl, The images of multilinear polynomials on strictly upper triangular matrices. 2019, 563, 287- 301.
11 FAGUNDES P S, MELLO T C D. Oper Matrices, Images of multilinear polynomials of degree up to four on upper triangular matrices. 2019, 13, 283- 292.
12 WANG Y. Linear Multilinear A, The images of multilinear polynomials on $ 2\times 2$ upper triangular matrix algebras . 2019, 67, 2366- 2372.
13 WANG Y, LIU P P, BAI J. Linear Multilinear A, Correction: The images of multilinear polynomials on $ 2\times 2$ upper triangular matrix algebras . 2019, 67, 2373- 2378.
14 CHEUNG W S. Linear Multilinear A, Lie derivations of triangular algebras. 2003, 51, 299- 310.
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