Images of multilinear polynomials of degree up to four on upper triangular matrices

TL;DR

This paper characterizes the images of multilinear polynomials of degree up to four when evaluated on upper triangular matrix algebras, providing insights into their algebraic structure.

Contribution

It offers a detailed description of the images of multilinear polynomials of degree up to four on upper triangular matrices, a topic not extensively covered before.

Findings

Descriptions of polynomial images on upper triangular matrices

Extension of known results to degree four polynomials

New algebraic characterizations of polynomial images

Abstract

We describe the images of multilinear polynomials of degree up to four on the upper triangular matrix algebra.