Mathematics

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

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.

Cite this article

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

References

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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