The image of polynomials in one variable on 2×2 upper triangular matrix algebras

Abstract

In the present paper, we give a description of the image of polynomials in one variable on 2×2 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 2×2 upper triangular matrix algebras over an algebraically closed field.

Keywords

• polynomial
• upper triangular matrix algebra
• algebraically closed field