The image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras

Lan Lu; Yu Wang; Huihui Wang; Haoliang Zhao; Lan Lu; Yu Wang; Huihui Wang; Haoliang Zhao

doi:10.3934/math.2022551

AIMS Mathematics

2022, Volume 7, Issue 6: 9884-9893. doi: 10.3934/math.2022551

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Research article

The image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras

1.
Department of Basic Courses, Changchun Guanghua University, Changchun 130033, China
2.
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

Received: 26 December 2021 Revised: 19 February 2022 Accepted: 27 February 2022 Published: 18 March 2022
MSC : 16S50, 16R10, 15A54

In the present paper, we give a description of the image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras over an algebraically closed field. As consequences, we give concrete descriptions of the images of polynomials of degrees up to $ 4 $ in one variable on $ 2\times 2 $ upper triangular matrix algebras over an algebraically closed field.
- polynomial,
- upper triangular matrix algebra,
- algebraically closed field
Citation: Lan Lu, Yu Wang, Huihui Wang, Haoliang Zhao. The image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras[J]. AIMS Mathematics, 2022, 7(6): 9884-9893. doi: 10.3934/math.2022551

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Abstract

In the present paper, we give a description of the image of polynomials in one variable on $ 2\times 2 $ upper triangular matrix algebras over an algebraically closed field. As consequences, we give concrete descriptions of the images of polynomials of degrees up to $ 4 $ in one variable on $ 2\times 2 $ upper triangular matrix algebras over an algebraically closed field.

References

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