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

doi:10.3969/j.issn.1000-5641.201911047

Journal of East China Normal University(Natural Science) ›› 2021, Vol. 2021 ›› Issue (1): 8-15.doi: 10.3969/j.issn.1000-5641.201911047

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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

Abstract

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

CLC Number:

O153.3

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.

References 14

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

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